nLab
π-Kan condition

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

The π *\pi_\ast-Kan condition (Bousfield & Friedlander 1978, B.3) on a bisimplicial set guarantees that its geometric realization behaves well with respect to homotopy pullback (Bousfield & Friedlander 1978, Thm. B.4).

See also this Prop. at geometric realization of simplicial topological spaces.

References

Created on September 13, 2021 at 05:17:13. See the history of this page for a list of all contributions to it.