Burroni's \( T \)-categories generalize internal categories, which themselves generalize ordinary (small) categories. The classical nerve construction assigns to a small category a simplicial set, and this construction extends routinely to internal categories: any internal category in a...

Lax extensions (also called relators or relation liftings) are a categorical notion for reasoning about functors acting on functions and relations in a compatible way. They play a central role in developing sound proof principles for behavioral equivalence of state-based systems and are also...