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Results tagged with topos-theory
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user 126667
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,...
5
votes
What is neutral constructive mathematics
I don't know the history of the phrase "neutral constructive mathematics", but I would guess that it is meant to be analogous to "neutral geometry". Neutral geometry (or absolute geometry) is the part …
- 25.2k
12
votes
Accepted
Taking the category of sheaves is symmetric monoidal
Provided at least one of $M$ and $N$ is locally compact, the $\infty$-topos $\mathrm{Sh}(M \times N)$ is the product of $\mathrm{Sh}(M)$ and $\mathrm{Sh}(N)$ in $\mathrm{RTop}$. This is HTT 7.3.1.11. …
- 25.2k
4
votes
Accepted
Sheaves on sites given by a (regular) cd-structure
In general sections $b \in F(B)$ and $c \in F(C)$ that agree on $F(A)$ don't induce a matching family on $\{B \to D, C \to D\}$ though. The sheaf condition for that family is that
$$
F(D) \to F(B) \ti …
- 25.2k
48
votes
Accepted
Can a topos ever be an abelian category?
No. In fact no nontrivial cartesian closed category can have a zero object 0 (one which is both initial and final), as then for any X, 0 = 0 × X = X. (The first equality uses the fact that – × X com …
- 25.2k
10
votes
Accepted
Does sheafification preserve sheaves for a different topology?
I think my answer to this question provides a counterexample: Let C be the category a → b, and consider the topologies T1 generated by the single covering family {a → b} and T2 generated by declaring …
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