In any category, a cospan is a diagram like this:
A cospan in the category is the same as a span in the opposite category . So, all general facts about cospans in are general facts about spans in , and the reader may turn to the entry on spans to learn more.
A cospan that admits a cone is called a quadrable cospan.
Cospans in a category with small colimits form a bicategory whose objects are the objects of , whose morphisms are cospans between two objects, and whose 2-morphisms are commuting diagrams of the form
The category of cospans from to is naturally a category enriched in : for
two parallel cospans in , the -object of morphisms between them is the pullback
formed in analogy to the enriched hom of pointed objects. The initial object of is the coproduct of and .
If has a terminal object, , then cospans from to itself are bi-pointed objects in .
Topological cospans and their role as models for cobordisms are discussed in
Last revised on May 19, 2021 at 04:09:24. See the history of this page for a list of all contributions to it.