Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

Span categories provide an abstract framework for formalizing mathematical models of certain systems. The descriptions some systems, such as classical mechanical require that do not have pullbacks, and this limits the utility span a formal framework. Given $\mathscr{C}$ $\mathscr{C}^\prime$ functor $\mathcal F$ from to $\mathscr{C}^\prime$, we introduce notion pullback cospan in $\mathscr{C}$, ...

Abstract We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind enriched category. The base for enrichment is category commutative monoids—or in straightforward generalisation, modules over rig k . However, tensor product on this not usual one, but rather warping it by certain monoidal comonad Q Thus sense, skew sense Szlachányi. Our first main result ...

We give a 3-universal property for the Karoubi envelope of 2-category. Using this, we show that 3-categories finite semisimple 2-categories (as introduced in arXiv:1812.11933) and multifusion categories are equivalent.