Comma category information

In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms:...

abstractly as initial or terminal objects of a comma category (see § Connection with comma categories, below). Universal properties occur almost everywhere...

Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

The comma , is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation...

Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer...

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...

G)^{\text{op}}\cong (G^{\text{op}}\downarrow F^{\text{op}})} (see comma category) Dual object Dual (category theory) Duality (mathematics) Adjoint functor Contravariant...

In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

preserves the identity). (Note that this is precisely the definition of the comma category of R over the inclusion of unitary rings into rng.) The existence of...

monoidal category Braided monoidal category Topos Category of small categories Semigroupoid Comma category Localization of a category Enriched category Bicategory...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

In category theory, a branch of mathematics, a functor category D C {\displaystyle D^{C}} is a category where the objects are the functors F : C → D {\displaystyle...

object X to a functor U can be defined as an initial object in the comma category (X ↓ U). Dually, a universal morphism from U to X is a terminal object...

prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

maps as morphisms. Another way to think about this category is as the comma category, ( { ∙ } ↓ {\displaystyle \{\bullet \}\downarrow } Top) where { ∙ }...

In category theory, a branch of mathematics, a closed category is a special kind of category. In a locally small category, the external hom (x, y) maps...

In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...