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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,...
0
votes
0
answers
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 …
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 …
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 …