Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
In a 2-category, the horizontal composition of a 2-morphism with 1-morphisms is sometimes called whiskering.
Whiskering from the left with an equivalence and from the right with an inverse equivalence is a conjugation action of equivalences on 2-morphisms.
For instance in Cat whiskering is the composition of a functor with a natural transformation to produce a natural transformation. If we identify a functor or 1-morphism with its identity natural transformation or identity 2-morphism?, then whiskering is a special case of horizontal composition, and composition of 1-morphisms is a special case of whiskering.
- If and are functors and is a natural transformation whose coordinate at any object of is , then whiskering and yields the natural transformation whose coordinate at is .
- If and are functors and is a natural transformation whose coordinate at is , then whiskering and yields the natural transformation whose coordinate at is .
Revised on June 17, 2016 13:53:40
by Mike Shulman