nLab
Ho(∞Grpd)

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

(,1)(\infty,1)-Category theory

Contents

Idea

The homotopy category of an (∞,1)-category of ∞Grpd. equivalent to Ho(Top). Obtained as the localization of sSet at the weak homotopy equivalences. This is the classical homotopy category.

Properties

H-Monoids

A monoid object in Ho(Grpd)Ho(\infty Grpd) is an H-monoid.

A group object in Ho(Grpd)Ho(\infty Grpd) is an H-group.

category: category

Last revised on November 26, 2012 at 17:21:31. See the history of this page for a list of all contributions to it.