In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. ...

5 окт. 2024 г. · Direct categories versus finite simplicial sets. If a direct category has finitely many objects then its nerve is a finite simplicial set.

16 авг. 2016 г. · The usual definition of the nerve a category has as n-simplices strings of n composable morphisms; the vertices of such a simplex are the ... algebraic topology - two definitions of the nerve of a category Geometric realization of the nerve of a category and group ... internal hom between nerve of categories is nerve of functor ... Другие результаты с сайта math.stackexchange.com

The nerve of a category is among the most fundamental constructions in category theory for homotopy theorists, to the point that it is popular to identify a ...

In this section, we will study a different class of simplicial sets, which arise instead from the theory of categories.

6 янв. 2008 г. · The nerve construction is simple, clean, and links category theory to simplicial sets, which are important in topology and other areas.

21 мар. 2023 г. · Nerve and realization of categories · The induced nerve is the ∞-nerve. · The induced realization operation is the operation of forming the free ω ...

Recall that the nerve of a category is defined as: N : Cat → sSet. Nn(C) = F un(∆c.

18 июн. 2010 г. · From this we have constructed something that might be called a "span nerve" of a category. It receives a map from the usual nerve (given by a ... Simplicial nerve of a topological group - MathOverflow Classifying space as the geometric realization of the nerve of - G The simplicial Nerve - MathOverflow Does the nerve of a category have a right adjoint? - MathOverflow Другие результаты с сайта mathoverflow.net

19 нояб. 2021 г. · We show that the canonical homotopy theory of strict 2-categories embeds in that of -categories in the form of 2-(pre)complicial sets.