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
Simplicial homotopy theory is the study of homotopy theory by means of simplicial sets, but also the study of those properties of simplicial sets detectable by means of techniques adapted from topological homotopy theory.
A key tool is the classical model structure on simplicial sets.
homotopy hypothesis-theorem
Pierre Gabriel, Michel Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. Springer, New York (1967)
Edward Curtis, Simplicial Homotopy Theory, Advances in Math., 6, (1971), 107 – 209.
Paul Goerss, Rick Jardine, Simplicial homotopy theory, Progress in Mathematics, Birkhäuser (1996)
André Joyal, Myles Tierney An introduction to simplicial homotopy theory, 2005 (chapter I, more notes pdf)
Last revised on March 17, 2017 at 03:54:05. See the history of this page for a list of all contributions to it.