3 papers
math.CT2025
Colimits of internal categories
Calum Hughes, Adrian Miranda
We show that for an extensive -category with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \t…
math.CT2025
The algebraic internal groupoid model of Martin-Löf type theory
Calum Hughes
We extend the model structure on the category of internal categories studied by Everaert, Kieboom and Van der Linden to an algebraic model structure. Mo…
math.CT2024
The elementary theory of the 2-category of small categories
Calum Hughes, Adrian Miranda
We give an elementary description of -categories of internal categories, functors and natural transformations, where is a ca…