For an object in a category with coproducts, the codiagonal of (or fold morphism) is the canonical morphism
given by copairing the identity morphism with itself. The dual concept is diagonal . More generally, one can consider the iterated codiagonal
In a cartesian bicategory , the pair of terms diagonal, codiagonal refer to the canonical comultiplication and the dual multiplication on any object. While the comultiplication is not a true diagonal (because is not a cartesian product in ), it is the diagonal when seen as belonging to the subcategory of maps (left adjoints), where the restriction of to becomes a 2-product. Similarly, is not a true codiagonal on , but it becomes a codiagonal in the sense above when seen as belonging to , the opposite obtained by reversing -cells but not -cells.
The term ‘codiagonal’ is also sometimes used in the context of the theory of bisimplicial sets. For this use see total simplicial set, within that entry.
Last revised on March 6, 2023 at 23:53:48. See the history of this page for a list of all contributions to it.