simplicial category

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• Simplicial category — In mathematics, the simplicial category (or ordinal category) is a construction in category theory used to define simplicial and cosimplicial objects. Formal definitionThe simplicial category is usually denoted by Delta and is sometimes denoted… …   Wikipedia

• Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… …   Wikipedia

• Simplicial manifold — In mathematics, the term simplicial manifold commonly refers to either of two different types of objects, which combine attributes of a simplex with those of a manifold. Briefly; a simplex is a generalization of the concept of a triangle into… …   Wikipedia

• PRO (category theory) — In category theory, a PRO is a strict monoidal category whose objects are the natural integers and whose tensor product is given on objects by the addition on integers. By an integer n, we mean here the set {0,1,ldots,n 1}.Some examples of PROs:… …   Wikipedia

• Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

• Nerve (category theory) — In category theory, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C …   Wikipedia

• Abstract simplicial complex — In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of finite sets closed under the operation of taking subsets. In the context of matroids… …   Wikipedia

• Higher category theory — is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Contents 1 Strict higher categories 2 Weak higher… …   Wikipedia

• Accessible category — The theory of accessible categories was introduced in 1989 by mathematicians Michael Makkai and Robert Paré in the setting of category theory. Their motivation was model theoretic, a branch of mathematical logic.J. Rosicky… …   Wikipedia

• End (category theory) — Not to be confused with the use of End to represent (categories of) endomorphisms. In category theory, an end of a functor is a universal dinatural transformation from an object e of X to S. More explicitly, this is a pair (e,ω), where e is an… …   Wikipedia

• A¹ homotopy theory — In algebraic geometry and algebraic topology, a branch of mathematics, A1 homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to… …   Wikipedia