nLab homotopy quotient

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.

Related concepts

• subquotient

• quotient space, geometric invariant theory

• action groupoid, quotient stack, global quotient orbifold

• BRST complex

• In type theory/homotopy type theory the analogous concept is that of quotient types.

• derived intersection