nLab
simplicial weak equivalence

Contents

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

A simplicial weak equivalence is a weak equivalence in the standard homotopy theory of simplicial sets, hence with respect to the classical model structure on simplicial sets.

Definition

A morphism ff between simplicial sets is a simplicial weak equivalence if any of the following equivalent conditions is satisfied (where Ex Ex^\infty denotes Kan fibrant replacement):

Last revised on July 10, 2021 at 15:55:09. See the history of this page for a list of all contributions to it.