Adrian Miranda

collaborators

3 papers

math.CT2025

Colimits of internal categories

Calum Hughes, Adrian Miranda

We show that for an extensive $1$ -category $E$ with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \t…

math.CT2024

A semi-strictly generated closed structure on Gray-Cat

Adrian Miranda

We show that the semi-strictly generated internal homs of $Gray$ -categories $[A, B]_{ssg}$ defined in \cite{Miranda strictifying operational coh…

math.CT2024

The elementary theory of the 2-category of small categories

Calum Hughes, Adrian Miranda

We give an elementary description of $2$ -categories $Cat (E)$ of internal categories, functors and natural transformations, where $E$ is a ca…