Distributivity Pullback

For morphisms $a,:{{}(X,A)},f:{{}(A,B)}$ pullback around $a,f$ is a diagram

such that the outer square is a Pullback.

A distributivity pullback is the Terminal such pullback, where a morphism of pullbacks around $a,f$ looks like

Properties

• A morphism $f:{{}(A,B)}$ is an Exponential Object in the Slice Category $\mathcal{C}/A$ if and only if all distributivity pullbacks along $f$ exist.

References

• https://ncatlab.org/nlab/show/distributivity+pullback
• Weber, Mark. “Polynomials in Categories with Pullbacks.” arXiv, May 21, 2015. https://doi.org/10.48550/arXiv.1106.1983.