nLab Homotopy Types

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

This page compiles pointers related to:

on homotopy theory with focus on the notion of homotopy types.

It starts from a basic position and attacks three main topics:

Contents

What are homotopy types?

How to build homotopy types

Whitehead’s realization problem

Algebraic models of nn-types

Cohomology of groups and cohomology of categories

Simply connectd homotopy types and HπH\pi-duality

The Hurewicz homomorphism

Postnikov invariants and boundary invariants

The classification theorems

Stable homotopy types

Decomposition of stable homotopy types

Localization

References

category: reference

Last revised on January 2, 2023 at 15:11:27. See the history of this page for a list of all contributions to it.