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

homotopy category of topological spaces. Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets...

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

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

closed. The simplex category can be used to construct an example of non-symmetric compact closed category. The simplex category is the category of non-zero...

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...

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

In category theory, a branch of mathematics, the opposite category or dual category C op {\displaystyle C^{\text{op}}} of a given category C {\displaystyle...

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

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

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...

specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex...

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...

precisely a simple object in the category of (say left) modules. simplex category The simplex category Δ is the category where an object is a set [n] =...

Applied category theory Category of sets Concrete category Category of vector spaces Category of graded vector spaces Category of chain complexes Category of...

} f)(x) ≃ F(g)(F(f)(x)), where x ≃ y means x ≤ y and y ≤ x. FinOrd Simplex category Eklund et al. 2018, Section 1.3. "PreOrd in nLab". ncatlab.org. Clementino...

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...

nerve N h c ( C ) {\displaystyle N^{hc}(C)} of a 2-category C is a simplicial set where each n-simplex is determined by the following data: n objects x...

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...

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

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, the Yoneda lemma is a fundamental result in category theory. It is an abstract result on functors of the type morphisms into a fixed object...

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...

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...