Bridge in a Double Category

A bridge in a Double Category $\mathcal{D}$ is a diagram $I\xrightarrow{p}A\xrightarrow{t}J$.

Examples

• In the Pseudo Double Category of Spans, a bridge is a diagram $I\leftarrow E\to B\to J$, which is precisely the data of an Indexed Polynomial Functor.

References

• Nathanael Arkor: “A (Virtual) Double Category Theorist’s Perspective on Polynomials,” 2025. https://www.youtube.com/watch?v=tCbRfjv6JQ4.