nLab
cospan

Definition

In any category, a cospan is a diagram like this:

$$\begin{array}{ccccccc}& & a& & & & b\\ & & & {}_f\searrow & & {\swarrow }_g& & \\ & & & & c& & & & \end{array}$$\array{ && a &&&& b \\ & && {}_{f}\searrow & & \swarrow_g && \\ &&&& c &&&& }

A cospan that admits a cone is called a quadrable cospan.

A cospan in the category $C$ is the same as a span in the opposite category $C^{\mathrm{op}}$. So, all general facts about cospans in $C$ are general facts about spans in $C^{\mathrm{op}}$, and the reader may turn to the entry on spans to learn more.

See also

• Cospans in Algebraic Topology
• multispan
• the cograph of a function
• the cograph of a functor