A transfor between pseudo/lax natural transformations is sometimes called a modification. Hence modifications are the 3-morphisms in a 3-category 2Cat of 2-categories and 2-functors between them.
Just as a natural transformation between functors is a collection of -cells indexed by -cells, a modification between transformations is an indexed collection of 2-cells.
To be most general, start with lax transformations . Given those, a modification assigns to each -cell a -cell in that commutes suitably with the -cell components of and (see Leinster for details).
If are strict transformations, then the complicated-looking modification condition becomes simply a naturality square with globs where the -cells would normally be.
When you get tired of thinking individually about -categories, functors, transformations, modifications, and so on, check out (n,k)-transformation.
(Some discussion from here has also been moved to there.)
Last revised on July 6, 2018 at 14:13:36. See the history of this page for a list of all contributions to it.