In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving...

ordered sets and categories. Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets. Simplicial...

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...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

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 mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked...

Herpes simplex, often known simply as herpes, is a viral infection caused by the herpes simplex virus. Herpes infections are categorized by the area of...

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...

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

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

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

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

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

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

simplicial sets, which are presheaves on the simplex category). If C is a model category, then so is the category Pro(C) of pro-objects in C. However, a model...

For example, by definition, a simplicial set is a presheaf on the simplex category Δ and a representable simplicial set is exactly of the form Δ n = Hom...

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...

0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron...

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, 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, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e...

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...

presheaf on the simplex category C = Δ {\displaystyle C=\Delta } . When C {\displaystyle C} is a small category, the functor category C ^ = S e t C o...

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

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

cokernel is called the corank of f. Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps...

has the relaxed properties: ∀x ∈ F(A), F(idA)(x) ≃ x, ∀x ∈ F(A), F(g∘f)(x) ≃ F(g)(F(f)(x)), where x ≃ y means x ≤ y and y ≤ x. FinOrd Simplex category...