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10 votes

Commutative rings : Topoi = Fields :?

This is a long comment. I would prefer to say that (Grothendieck) topoi are "(some) affine schemes over $\text{Spec } \text{Set}$." Here is my preferred version of the table, sprinkle $\infty$s accord …
Qiaochu Yuan's user avatar
5 votes
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Is the infinity-groupoid of a finite CW complex finitely-presented?

A CW structure is precisely a presentation of an $\infty$-groupoid, and so "finite CW complex" means precisely "finitely presented $\infty$-groupoid."
Qiaochu Yuan's user avatar