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A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...
4
votes
Topological vs pro fundamental groups
I figured my comments are getting too long so I should put some of them here, even though I'm using a different topology on $\pi_1$ (often it is the same, but certainly not always) and a possibly diff …