# nLab rectification

Contents

### Context

#### Higher category theory

higher category theory

# 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 11:11:11. See the history of this page for a list of all contributions to it.