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
Given a homotopy theory, i.e. an (infinity,1)-category, then a tower of homotopy fibers or tower of fibrations or similar is a tower diagram of the form
where each hook is a homotopy fiber sequence.
The long exact sequences of homotopy groups for each of the hooks in the tower combine to yield an exact couple. The corresponding spectral sequence of an exact couple is a means to (approximately) compute the homotopy groups of the base object $X$ of the tower
Aldridge Bousfield, Daniel Kan, chapter IX of Homotopy limits, completions and localization, Springer 1972
Paul Goerss, Rick Jardine, chapter VI of Simplicial homotopy theory, 1996
Last revised on October 15, 2019 at 09:19:50. See the history of this page for a list of all contributions to it.