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
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 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)
Donald Werner Anderson, Fibrations and geometric realization, Bull. Amer. Math. Soc. Volume 84, Number 5 (1978), 765-788. (euclid:1183541139)
Jacob Lurie, Simplicial spaces, Lecture 7 of: Algebraic L-theory and Surgery, 2011 (pdf)
Charles Rezk, When are homotopy colimits compatible with homotopy base change?, 2014 (pdf, pdf)
Edoardo Lanari, Compatibility of homotopy colimits and homotopy pullbacks of simplicial presheaves (pdf, pdf)
(expanded version of Rezk 14)
Aaron Mazel-Gee, Model -categories I: some pleasant properties of the -category of simplicial spaces (arXiv:1412.8411)
Jacob Lurie, around Lem. 5.5.6.17 in: Higher Algebra (~2017)
Jacob Lurie, Thms. A.5.4.1, Spectral Algebraic Geometry (2018) [pdf]
Daniel Berwick-Evans, Pedro Boavida, Dmitri Pavlov, §3 of: Classifying spaces of infinity-sheaves, Algebraic & Geometric Topology [arXiv:1912.10544]
Last revised on October 15, 2023 at 09:04:12. See the history of this page for a list of all contributions to it.