ordinary category theory. An enriched category with hom-objects from monoidal category M is said to be an enriched category over M or an enriched category in...

other enriched models like topologically enriched categories. Topologically enriched categories (sometimes simply called topological categories) are categories...

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...

mathematics, a simplicially enriched category, is a category enriched over the category of simplicial sets. Simplicially enriched categories are often also called...

the following "piecemeal" definition: A category is preadditive if it is enriched over the monoidal category Ab of abelian groups. This means that all...

also used in the definition of an enriched category. Monoidal categories have numerous applications outside of category theory proper. They are used to...

more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of abelian groups (equivalently...

equations. A category C is preadditive if all its hom-sets are abelian groups and composition of morphisms is bilinear; in other words, C is enriched over the...

of categories. Category Functor Natural transformation Homological algebra Diagram chasing Topos theory Enriched category theory Higher category theory...

Mathematics portal Domain theory Enriched category theory Glossary of category theory Group theory Higher category theory Higher-dimensional algebra...

In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the...

formulated in the category of sets). A topos can also be used to represent a logical theory. Mathematics portal Enriched category Higher category theory Quantaloid...

Look up enrichment or enrich in Wiktionary, the free dictionary. Enrichment or enriched may refer to: Data enrichment, appending data with context from...

carries the structure of a category. It can be formally defined as a category enriched over Cat (the category of categories and functors, with the monoidal...

Tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...

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

of (∞, 1)-categories, including Segal category, simplicially enriched category, topological category, complete Segal space. A quasi-category is also an...

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...

In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

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

the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept...

In mathematics, specifically category theory, a subcategory of a category C is a category S whose objects are objects in C and whose morphisms are morphisms...

common throughout category theory for any binary equaliser. In the case of a preadditive category (a category enriched over the category of Abelian groups)...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence...

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences'...

functors preserve limits. For example, if a metric space is viewed as an enriched category (see generalized metric space), then the Cauchy completion of it coincides...