Post #1815099

2024-07-04 13:56 UTC

@johncarlosbaez Anyways, it's funny that I made this mistake, since in a lot of ways the topological topos solves the same problems as condensed sets, so I should probably have profinite topologies closer to the front of my mind when thinking about examples!

Replies (1)

@johncarlosbaez@mathstodon.xyz 2024-07-04 14:24

@hallasurvivor - Various people have argued that "topological space" is a kind of big tent, or compromise, that people chose to handle a number of quite different tasks. I forget who these people are, but it sounds true. I'm glad Scholze is trying to map out the different tasks and propose substitutes optimized for these different tasks. I'm afraid this is going to be tough. For you - or maybe him? - locales are obviously THE right thing to consider if you're doing pointset topology. But those hidebound traditionalists, the pointset topologists, may cling to working with spaces that are sets of points. 😏 But never mind them. What's an animus, exactly? Is it supposed to be some more mystical-sounding synonym for infinity-groupoid or homotopy type, or is it something more specific?

Open ##1815100