Post #1905748
2026-04-23 21:13 UTC
@maxsnew Yes — and Uemura has already begun to develop synthetic topos theory using this analogy. There are other recent perspectives that may also be of interest, which perhaps @olynch can comment on…
Replies (1)
-
@olynch@mathstodon.xyz 2026-04-24 07:12
@jonmsterling @maxsnew The intuition for a general set is a set whose elements are finitely constructable. Finite limits and initial algebra constructions preserve this property. The tricky thing with topos theory is that it depends on an underlying set theory to index infinite colimits, which is why Vickers shifted from topoi to arithmetic universes while developing this perspective.