nLab rectification

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

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

In homotopy theory and in higher category theory by rectification one (usually, often) means the equivalent presentation of a homotopy-coherent structure equivalently by apparently more naive “strict” data.

Many or most rectification statements are examples of the general Rectification theorem for algebras over an operad which states sufficient conditions for the category of algebras over an operad to already be Quillen equivalent to that of the corresponding ∞-algebras over an (∞,1)-operad.

This includes notably Vogt's theorem on the rectification of homotopy coherent diagrams.

Examples

Last revised on July 23, 2021 at 15:11:11. See the history of this page for a list of all contributions to it.