nLab
homotopical functor

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

Contents

Definition

A homotopical functor F:CDF : C \to D between two homotopical categories CC and DD is a functor which preserves the weak equivalences of CC (i.e., which sends all weak equivalences of CC to weak equivalences of DD).

Revised on March 30, 2016 04:21:33 by Urs Schreiber (31.55.43.247)