nLab
natural isomorphism

Context

Category theory

Equality and Equivalence

Contents

Definition

A natural isomorphism η:FG\eta\colon F \Rightarrow G between two functors FF and GG

F C η D G \array{ & \nearrow \searrow^{F} \\ C &{}^{\simeq}\Downarrow^\eta& D \\ & \searrow \nearrow_{G} }

is equivalently

In this case, we say that FF and GG are naturally isomorphic.

If you want to speak of ‘the’ functor satisfying certain conditions, then it should be unique up to unique natural isomorphism.

A natural isomorphism from a functor to itself is also called a natural automorphism.

Revised on April 1, 2013 15:08:18 by Urs Schreiber (89.204.130.66)