nLab equivalence of infinity-groupoids


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



Paths and cylinders

Homotopy groups

Basic facts


Equality and Equivalence

An equivalence in an (∞,1)-category in ∞Grpd, hence ann equivalence of (∞,1)-categories between (∞,1)-categories that happen to be ∞-groupoids.

In terms of presentation by topological spaces or simplicial sets (see at homotopy hypothesis) this is a weak homotopy equivalence.

In terms of presentation by CW-complexes or Kan complexes, it is a homotopy equivalence.

Last revised on January 8, 2016 at 10:59:44. See the history of this page for a list of all contributions to it.