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1Abstract Elementary Classes And Accessible Categories

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We compare abstract elementary classes of Shelah with accessible categories having directed colimits.

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  • Title: ➤  Abstract Elementary Classes And Accessible Categories
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  • Language: English

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2Approximations Of Superstability In Concrete Accessible Categories

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We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms. In particular, we prove that if any category of this form is categorical in a successor, directed colimits of saturated objects are themselves saturated.

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  • Title: ➤  Approximations Of Superstability In Concrete Accessible Categories
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  • Language: English

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3Locally Class-presentable And Class-accessible Categories

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We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the abstract homotopy theory.

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  • Title: ➤  Locally Class-presentable And Class-accessible Categories
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  • Language: English

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4Definable Orthogonality Classes In Accessible Categories Are Small

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We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Levy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) is provable in ZFC if S is \Sigma_1, while it follows from the existence of a proper class of supercompact cardinals if S is \Sigma_2, and from the existence of a proper class of what we call C(n)-extendible cardinals if S is \Sigma_{n+2} for n bigger than or equal to 1. These cardinals form a new hierarchy, and we show that Vopenka's principle is equivalent to the existence of C(n)-extendible cardinals for all n. As a consequence, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This result follows from the fact that cohomology equivalences are \Sigma_2. In contrast with this fact, homology equivalences are \Sigma_1, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC.

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  • Title: ➤  Definable Orthogonality Classes In Accessible Categories Are Small
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  • Language: English

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5Metric Abstract Elementary Classes As Accessible Categories

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We show that metric abstract elementary classes (mAECs) are, in the sense of [LR] (i.e. arXiv:1404.2528), coherent accessible categories with directed colimits, with concrete $\aleph_1$-directed colimits and concrete monomorphisms. More broadly, we define a notion of $\kappa$-concrete AEC---an AEC-like category in which only the $\kappa$-directed colimits need be concrete---and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah's Presentation Theorem and a proof of the existence of an Ehrenfeucht-Mostowski functor in case the category is large. For mAECs in particular, arguments refining those in [LR] yield a proof that any categorical mAEC is $\mu$-d-stable in many cardinals below the categoricity cardinal.

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  • Title: ➤  Metric Abstract Elementary Classes As Accessible Categories
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  • Language: English

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6Accessible Model Categories

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We prove that a weak factorization system on a locally presentable category is accessible if and only if it is small generated in the sense of R. Garner. Moreover, we discuss an analogy of Smith's theorem for accessible model categories.

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  • Language: English

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7Colimits Of Accessible Categories

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We show that any directed colimit of acessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals, any directed colimit of acessible categories and accessible embeddings is accessible.

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  • Title: ➤  Colimits Of Accessible Categories
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8Classification Theory For Accessible Categories

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We show that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits. In particular, we prove a generalization of a recent result of Boney on tameness under a large cardinal assumption. We also show that such categories support a robust version of the Ehrenfeucht-Mostowski construction. This analysis has the added benefit of producing a purely language-free characterization of AECs, and highlights the precise role played by the coherence axiom.

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9Compactly Accessible Categories And Quantum Key Distribution

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Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum key distribution, that rely on the law of large numbers. To overcome this limitation, we introduce the notion of a compactly accessible category, relying on the extra structure of a factorisation system. This notion allows for infinite dimension while retaining key properties of compact categories: the main technical result is that the choice-of-duals functor on the compact part extends canonically to the whole compactly accessible category. As an example, we model a quantum key distribution protocol and prove its correctness categorically.

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  • Language: English

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10Final Coalgebras In Accessible Categories

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We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p. categories to which our results apply. We rely on ideas developed by Tom Leinster for the study of self-similar objects in topology.

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11ERIC ED630675: Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers. Third Edition Language Is Not Static. It Flows Like A River In Response To The Riverbank And The Rocks That Border And Run Beneath It. In The Same Way, Glossaries Are Dynamic Expressions Of Current Language Usage. Developmental Education And Learning Assistance Have Changed Dramatically In Recent Years, And So Must Also The Language Used To Describe And Define Them. This Glossary Is Useful For The Wide Field Of Educators Involved With Promoting Student Success. It Provides Precise Language And Definitions To Use When Communicating With Peers And More Effectively Influencing Administrators, Legislators, And The Media. Some Of These Glossary Terms Are Emerging With Frequent Use While Others Are Declining. This Is Why This Glossary Is Not Static And Future Editions Will Continue To Reflect The Changes In Language. Based On Advice From Some Of The Reviewers To Make This Glossary More Accessible To Readers, I Reorganized It Into Different Topical Categories Rather Than A Traditional Alphabetical Order. I Hope This Format Will Not Only Make It Easier To Locate A Particular Glossary Term, But Also Discover Related Terms In The Same Category. The Nine Glossary Categories Are: (1) Teaching And Learning Process; (2) Antiracism And Racism; (3) Assessment; (4) Copyright And Academic Integrity; (5) Pedagogies For Teaching And Learning; (6) Program Management; (7) Student-to-student Learning; (8) Transitional Courses And Programs; And (9) Less Acceptable Glossary Terms. This Third Edition Of The Glossary Of Developmental Education And Learning Assistance Terms Has Dramatically Changed Since The Last Edition 14 Years Ago. For That Reason, The Name Of This Glossary Has Changed And Reflects Its Use In The Wider Education Community. These Terms Could Be Useful For Educators Working In Learning Assistance, Learning Centers, Developmental-level Courses, First-year Experience Courses And Programs, Orientation Courses And Programs, Federally-funded TRIO And Other Equity Programs, And Instructors Teaching First-year And Subsequent Courses In The General Course Curriculum. In Recognition Of The Expanded Scope Of This Glossary And Broader Utility For Other Members Involved With Postsecondary Education, The Glossary Title Has Become More Inclusive, "Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers." [This Paper Was Prepared For The College Reading And Learning Association.]

By

Language is not static. It flows like a river in response to the riverbank and the rocks that border and run beneath it. In the same way, glossaries are dynamic expressions of current language usage. Developmental education and learning assistance have changed dramatically in recent years, and so must also the language used to describe and define them. This glossary is useful for the wide field of educators involved with promoting student success. It provides precise language and definitions to use when communicating with peers and more effectively influencing administrators, legislators, and the media. Some of these glossary terms are emerging with frequent use while others are declining. This is why this glossary is not static and future editions will continue to reflect the changes in language. Based on advice from some of the reviewers to make this glossary more accessible to readers, I reorganized it into different topical categories rather than a traditional alphabetical order. I hope this format will not only make it easier to locate a particular glossary term, but also discover related terms in the same category. The nine glossary categories are: (1) teaching and learning process; (2) antiracism and racism; (3) assessment; (4) copyright and academic integrity; (5) pedagogies for teaching and learning; (6) program management; (7) student-to-student learning; (8) transitional courses and programs; and (9) less acceptable glossary terms. This third edition of the glossary of developmental education and learning assistance terms has dramatically changed since the last edition 14 years ago. For that reason, the name of this glossary has changed and reflects its use in the wider education community. These terms could be useful for educators working in learning assistance, learning centers, developmental-level courses, first-year experience courses and programs, orientation courses and programs, federally-funded TRIO and other equity programs, and instructors teaching first-year and subsequent courses in the general course curriculum. In recognition of the expanded scope of this glossary and broader utility for other members involved with postsecondary education, the glossary title has become more inclusive, "Essential Glossary for Increasing Postsecondary Student Success: Administrators, Faculty, Staff, and Policymakers." [This paper was prepared for the College Reading and Learning Association.]

“ERIC ED630675: Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers. Third Edition Language Is Not Static. It Flows Like A River In Response To The Riverbank And The Rocks That Border And Run Beneath It. In The Same Way, Glossaries Are Dynamic Expressions Of Current Language Usage. Developmental Education And Learning Assistance Have Changed Dramatically In Recent Years, And So Must Also The Language Used To Describe And Define Them. This Glossary Is Useful For The Wide Field Of Educators Involved With Promoting Student Success. It Provides Precise Language And Definitions To Use When Communicating With Peers And More Effectively Influencing Administrators, Legislators, And The Media. Some Of These Glossary Terms Are Emerging With Frequent Use While Others Are Declining. This Is Why This Glossary Is Not Static And Future Editions Will Continue To Reflect The Changes In Language. Based On Advice From Some Of The Reviewers To Make This Glossary More Accessible To Readers, I Reorganized It Into Different Topical Categories Rather Than A Traditional Alphabetical Order. I Hope This Format Will Not Only Make It Easier To Locate A Particular Glossary Term, But Also Discover Related Terms In The Same Category. The Nine Glossary Categories Are: (1) Teaching And Learning Process; (2) Antiracism And Racism; (3) Assessment; (4) Copyright And Academic Integrity; (5) Pedagogies For Teaching And Learning; (6) Program Management; (7) Student-to-student Learning; (8) Transitional Courses And Programs; And (9) Less Acceptable Glossary Terms. This Third Edition Of The Glossary Of Developmental Education And Learning Assistance Terms Has Dramatically Changed Since The Last Edition 14 Years Ago. For That Reason, The Name Of This Glossary Has Changed And Reflects Its Use In The Wider Education Community. These Terms Could Be Useful For Educators Working In Learning Assistance, Learning Centers, Developmental-level Courses, First-year Experience Courses And Programs, Orientation Courses And Programs, Federally-funded TRIO And Other Equity Programs, And Instructors Teaching First-year And Subsequent Courses In The General Course Curriculum. In Recognition Of The Expanded Scope Of This Glossary And Broader Utility For Other Members Involved With Postsecondary Education, The Glossary Title Has Become More Inclusive, "Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers." [This Paper Was Prepared For The College Reading And Learning Association.]” Metadata:

  • Title: ➤  ERIC ED630675: Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers. Third Edition Language Is Not Static. It Flows Like A River In Response To The Riverbank And The Rocks That Border And Run Beneath It. In The Same Way, Glossaries Are Dynamic Expressions Of Current Language Usage. Developmental Education And Learning Assistance Have Changed Dramatically In Recent Years, And So Must Also The Language Used To Describe And Define Them. This Glossary Is Useful For The Wide Field Of Educators Involved With Promoting Student Success. It Provides Precise Language And Definitions To Use When Communicating With Peers And More Effectively Influencing Administrators, Legislators, And The Media. Some Of These Glossary Terms Are Emerging With Frequent Use While Others Are Declining. This Is Why This Glossary Is Not Static And Future Editions Will Continue To Reflect The Changes In Language. Based On Advice From Some Of The Reviewers To Make This Glossary More Accessible To Readers, I Reorganized It Into Different Topical Categories Rather Than A Traditional Alphabetical Order. I Hope This Format Will Not Only Make It Easier To Locate A Particular Glossary Term, But Also Discover Related Terms In The Same Category. The Nine Glossary Categories Are: (1) Teaching And Learning Process; (2) Antiracism And Racism; (3) Assessment; (4) Copyright And Academic Integrity; (5) Pedagogies For Teaching And Learning; (6) Program Management; (7) Student-to-student Learning; (8) Transitional Courses And Programs; And (9) Less Acceptable Glossary Terms. This Third Edition Of The Glossary Of Developmental Education And Learning Assistance Terms Has Dramatically Changed Since The Last Edition 14 Years Ago. For That Reason, The Name Of This Glossary Has Changed And Reflects Its Use In The Wider Education Community. These Terms Could Be Useful For Educators Working In Learning Assistance, Learning Centers, Developmental-level Courses, First-year Experience Courses And Programs, Orientation Courses And Programs, Federally-funded TRIO And Other Equity Programs, And Instructors Teaching First-year And Subsequent Courses In The General Course Curriculum. In Recognition Of The Expanded Scope Of This Glossary And Broader Utility For Other Members Involved With Postsecondary Education, The Glossary Title Has Become More Inclusive, "Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers." [This Paper Was Prepared For The College Reading And Learning Association.]
  • Author:
  • Language: English

“ERIC ED630675: Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers. Third Edition Language Is Not Static. It Flows Like A River In Response To The Riverbank And The Rocks That Border And Run Beneath It. In The Same Way, Glossaries Are Dynamic Expressions Of Current Language Usage. Developmental Education And Learning Assistance Have Changed Dramatically In Recent Years, And So Must Also The Language Used To Describe And Define Them. This Glossary Is Useful For The Wide Field Of Educators Involved With Promoting Student Success. It Provides Precise Language And Definitions To Use When Communicating With Peers And More Effectively Influencing Administrators, Legislators, And The Media. Some Of These Glossary Terms Are Emerging With Frequent Use While Others Are Declining. This Is Why This Glossary Is Not Static And Future Editions Will Continue To Reflect The Changes In Language. Based On Advice From Some Of The Reviewers To Make This Glossary More Accessible To Readers, I Reorganized It Into Different Topical Categories Rather Than A Traditional Alphabetical Order. I Hope This Format Will Not Only Make It Easier To Locate A Particular Glossary Term, But Also Discover Related Terms In The Same Category. The Nine Glossary Categories Are: (1) Teaching And Learning Process; (2) Antiracism And Racism; (3) Assessment; (4) Copyright And Academic Integrity; (5) Pedagogies For Teaching And Learning; (6) Program Management; (7) Student-to-student Learning; (8) Transitional Courses And Programs; And (9) Less Acceptable Glossary Terms. This Third Edition Of The Glossary Of Developmental Education And Learning Assistance Terms Has Dramatically Changed Since The Last Edition 14 Years Ago. For That Reason, The Name Of This Glossary Has Changed And Reflects Its Use In The Wider Education Community. These Terms Could Be Useful For Educators Working In Learning Assistance, Learning Centers, Developmental-level Courses, First-year Experience Courses And Programs, Orientation Courses And Programs, Federally-funded TRIO And Other Equity Programs, And Instructors Teaching First-year And Subsequent Courses In The General Course Curriculum. In Recognition Of The Expanded Scope Of This Glossary And Broader Utility For Other Members Involved With Postsecondary Education, The Glossary Title Has Become More Inclusive, "Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers." [This Paper Was Prepared For The College Reading And Learning Association.]” Subjects and Themes:

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Find ERIC ED630675: Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers. Third Edition Language Is Not Static. It Flows Like A River In Response To The Riverbank And The Rocks That Border And Run Beneath It. In The Same Way, Glossaries Are Dynamic Expressions Of Current Language Usage. Developmental Education And Learning Assistance Have Changed Dramatically In Recent Years, And So Must Also The Language Used To Describe And Define Them. This Glossary Is Useful For The Wide Field Of Educators Involved With Promoting Student Success. It Provides Precise Language And Definitions To Use When Communicating With Peers And More Effectively Influencing Administrators, Legislators, And The Media. Some Of These Glossary Terms Are Emerging With Frequent Use While Others Are Declining. This Is Why This Glossary Is Not Static And Future Editions Will Continue To Reflect The Changes In Language. Based On Advice From Some Of The Reviewers To Make This Glossary More Accessible To Readers, I Reorganized It Into Different Topical Categories Rather Than A Traditional Alphabetical Order. I Hope This Format Will Not Only Make It Easier To Locate A Particular Glossary Term, But Also Discover Related Terms In The Same Category. The Nine Glossary Categories Are: (1) Teaching And Learning Process; (2) Antiracism And Racism; (3) Assessment; (4) Copyright And Academic Integrity; (5) Pedagogies For Teaching And Learning; (6) Program Management; (7) Student-to-student Learning; (8) Transitional Courses And Programs; And (9) Less Acceptable Glossary Terms. This Third Edition Of The Glossary Of Developmental Education And Learning Assistance Terms Has Dramatically Changed Since The Last Edition 14 Years Ago. For That Reason, The Name Of This Glossary Has Changed And Reflects Its Use In The Wider Education Community. These Terms Could Be Useful For Educators Working In Learning Assistance, Learning Centers, Developmental-level Courses, First-year Experience Courses And Programs, Orientation Courses And Programs, Federally-funded TRIO And Other Equity Programs, And Instructors Teaching First-year And Subsequent Courses In The General Course Curriculum. In Recognition Of The Expanded Scope Of This Glossary And Broader Utility For Other Members Involved With Postsecondary Education, The Glossary Title Has Become More Inclusive, "Essential Glossary For Increasing Postsecondary Student Success: Administrators, Faculty, Staff, And Policymakers." [This Paper Was Prepared For The College Reading And Learning Association.] at online marketplaces:


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