#
nLab
enhanced factorisation system

Contents
### Context

#### Factorization systems

#### Category theory

**category theory**

## Concepts

## Universal constructions

## Theorems

## Extensions

## Applications

# Contents

## Definition

An **enhanced factorisation system** on a 2-category is an orthogonal factorisation system on a 2-category such that, for any invertible 2-cell $\alpha : t e \Rightarrow m s$

there is a unique pair of a 1-cell $r : B \to C$ and invertible 2-cell $\beta : t \Rightarrow m r$ such that $r e = s$ and $\beta e = \alpha$.

## References

Enhanced factorisation systems were defined in

attributed to Max Kelly.

Last revised on June 1, 2023 at 09:43:24.
See the history of this page for a list of all contributions to it.