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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,...

15 votes
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553 views

Constructing a topos from a Heyting algebra

It is true that, given any topos $\mathcal{C}$ with a terminal object $1_\mathcal{C}$, $Sub(1_\mathcal{C})$ is a Heyting algebra. Now suppose that we start with a Heyting algebra $H$. Is it always po …
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2 votes
0 answers
111 views

Internal characterization of topos validity

I'm using Goldblatt's "Topoi: A categorical analysis of logic" as an introduction to topos logic. At the end of chapter 6, he defines the validity of propositional formulas (I'm not concerned with fir …
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