Being impressed by Barr and Diaconescu paper entitled "Atomic Toposes" (https://www.math.mcgill.ca/barr/papers/atom.top.pdf), I would like to ask whether it makes sense to investigate "Atomistic Categories", namely categories such that for any object the corresponding poset of subobject is atomistic (namely every element is arbitrary join of atoms). Have these categories been studied, are there non-trivial exaples (the category of sets is an example, but I'm searching for other examples!)
2026-03-29 15:30:17.1774798217
On Atomistic Categories
36 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CATEGORY-THEORY
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