Australian Category Seminar

If $\mathcal{V}$ is a monoidal category whose tensor product preserves reflexive coequalisers in each variable, then there is a bicategory $\mathbf{Comod}(\mathcal{V})$ of comonoids and comodules in $\mathcal{V}$. An example of this is where $\mathcal{V} = \mathbf{Poly}$, the category of polynomial endofunctors of $\mathbf{Set}$, for which it turns out that $\mathbf{Comod}(\mathbf{Poly})$ is equivalent to $\mathbf{PRA}$, the bicategory of parametric right adjoint functors between presheaf categories. I figured this out in 2020 in a very hands on way; this talk is about the slick way of doing this via the paper best known around here as [18].