nLab
simplicial homotopy theory

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

Simplicial homotopy theory is the study of homotopy theory by means of simplicial sets, but also the study of those properties of simplicial sets detectable by means of techniques adapted from topological homotopy theory.

A key tool is the classical model structure on simplicial sets.

References

(See also the references at homotopy theory, algebraic topology and ( , 1 ) (\infty,1) -category theory.)

Last revised on September 21, 2021 at 08:14:02. See the history of this page for a list of all contributions to it.