## View abstract

### Session S27 - Categories and Topology

Wednesday, July 21, 17:00 ~ 17:30 UTC-3

## Exponentiable Inclusions: Quantaloids and Ringoids

### Susan Niefield

In this talk, we will show that if $\cal V$ is a cocomplete symmetric monoidal category, then categories enriched in $\cal V$ are the objects of a double category with the appropriate glueing properties, and hence, we obtain the exponentiability of locally closed inclusions of $\cal V$-categories. Furthermore, we will see that the locally closed condition is also necessary when $\cal V$ is monadic over the category of sets. Thus, we obtain a characterization of the exponentiable inclusions of quantaloids (respectively, ringoids) when $\cal V$ is the category of suplattices (respectively, abelian groups) analogous to that of the five earlier cases.