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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,...

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299 views

nPOV: Cohomology and derived functors

In the nPOV, cohomology is realized as the connected component of the derived hom space [1]. Namely, $$H^n(X,Y) = \pi_0 \mathbb{H}(X,B^nY),$$ where $\mathbb{H}$ is an $(\infty,1)$-topos and $B$ is the …
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9 votes
2 answers
2k views

Truth in a different universe of sets?

I understand that provability and truth as different concepts. Provability is syntactic, it only concerns whether the given sentence can be derived by reiterating the inference rules over a collection …
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8 votes
1 answer
1k views

What's the point of a point-free locale?

In [1, example C.1.2.8], a locale $Y$ (dense in another locale $X$) without any point is given. I fail to understand the point of such point-less locale - Why can't we identify those as the trivial lo …
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