nLab
homotopy quotient

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 homotopy quotient is a quotient (say of a group action) in the context of homotopy theory.

Just as a quotient is a special case of colimit, so a homotopy quotient is a special case of homotopy colimit.

The homotopy quotient of a group action may be modeled by the corresponding action groupoid, which in the context of higher geometry means the corresponding quotient stack.

Last revised on April 12, 2018 at 17:03:01. See the history of this page for a list of all contributions to it.