Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
The triangle identities or zigzag identities are identities satisfied by the unit and counit of an adjunction.
Given (categories, or otherwise objects of a -category) with functors (or otherwise morphisms) and and natural isomorphisms (or otherwise -morphisms) and , the triangle identities are the following:
The RHS of the above diagrams have L and R interchanged. Furthermore, the LHS has C as target of L instead of D.
As string diagrams
In string diagrams, the identities appear as the action of “pulling zigzags straight” (hence the name):
With labels left implicit, this notation becomes very economical:
Revised on July 16, 2014 00:03:35