nLab
rectification

Context

Homotopy theory

, ,

flavors: , , , , , , , …

models: , , , …

see also

Introductions

Definitions

  • ,

  • ,

      • ,

Paths and cylinders

Homotopy groups

Basic facts

Theorems

  • -theorem

Higher category theory

Basic concepts

  • ,

Basic theorems

  • -theorem
  • -theorem
  • -theorem

Applications

Models

    • /
    • /
    • = (n,n)-category
      • ,
    • =
      • =
      • =
    • = (n,0)-category
      • ,
  • /

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.

Created on September 4, 2013 at 14:00:49. See the history of this page for a list of all contributions to it.