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
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The -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.
Aldridge Bousfield, Eric Friedlander, Homotopy theory of -spaces, spectra, and bisimplicial sets, Springer Lecture Notes in Math., Vol. 658, Springer, Berlin, 1978, pp. 80-130. (pdf, pdf)
Charles Rezk, When are homotopy colimits compatible with homotopy base change?, 2014 (i-hate-the-pi-star-kan-condition.pdf, pdf)
Created on September 13, 2021 at 09:17:13. See the history of this page for a list of all contributions to it.