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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

11 votes
Accepted

Product of topological spaces and product of corresponding locales

Your map $f$ is known to be an injective dense localic map. See, for example, Proposition 4.2.2 in [1]. In general, it isn't an isomorphism. The reason for this is that $\Omega(X \times_t Y)$ is quoti …
Tomáš Jakl's user avatar
17 votes
Accepted

Combination topological space and locale?

The proper term is topological system as found in Vickers' book Topology via Logic. Vickers actually uses precisely your expanded definition. What you call "topological" Vickers calls "spatial" and y …
Tomáš Jakl's user avatar
8 votes

Big list of comonads

The so-called game comonads have been recently studied in the context of finite model theory. The main references are the following: Samson Abramsky, Anuj Dawar, and Pengming Wang. "The pebbling como …