Post #1815108

@leemph It looks like I was combining two different mathoverflow posts in my mind. First, the comment from Peter Scholze on his answer here, saying that in his world "topology" is either anima, topoi, or condensed sets: https://mathoverflow.net/q/441610/145247 Then an answer here by Maxime Ramzi that says something similar: https://mathoverflow.net/q/459101/145247 As for what role plays the concept of "topos", remember that there's a very close connection between topoi and locales. Indeed, there's a fully faithful 2-embedding from locales to topoi, and this embedding admits a left adjoint ("localic reflection").