Explore: Representations Of Categories

viewed as particular kinds of categories, and the representations as functors from the object category to the category of vector spaces. This description

In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as

role. The universality of this ring says that the category of representations of a Lie algebra is the same as the category of modules over its enveloping

categories) to Quiv (the category of multidigraphs). Its left adjoint is a free functor which, from a quiver, makes the corresponding free category.

functions and values of grammatical categories. In linguistics, empty categories are represented with ∅. Symbolic representations also appear in phonetic

In category theory, two categories C and D are isomorphic if there exist functors F : C → D and G : D → C that are mutually inverse to each other, i.e

Collective representations are concepts, ideas, categories and beliefs that do not belong to isolated individuals, but are instead the product of a social

also refer to a category with a monoidal-category action. The categories of left and right modules are abelian categories. These categories have enough projectives

the theory of braided monoidal categories. Partly for this reason, braided monoidal categories and other topics are related in the theory of knot invariants

considered. For more details, please refer to the section on permutation representations. Other than a few marked exceptions, only finite groups will be considered