nLab
parameterized homotopy theory

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

Bundles

Contents

Idea

Parameterized (stable) homotopy theory is (stable) homotopy theory of bundles of homotopy types/stable homotopy types over a given base space.

For formalizations see at

References

A comprehensive textbook account on parameterized spectra in ∞Grpd \simeq L wheL_{whe}Top is in

A formulation of aspects of this in (∞,1)-category theory is in

Discussion of convenient model category presentations:

Last revised on November 1, 2019 at 03:52:48. See the history of this page for a list of all contributions to it.