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Results tagged with topos-theory
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user 483446
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,...
4
votes
Strong extensionality of 'membership' relation defined on the set of all morphisms of a well...
By definition of your relation $\in_C$, only for the morphisms into the terminal object $b:A \to 1$ are there morphisms $a:1 \to A$ such that $a \in_C b$, and $a$ by definition has to be a global elem …
- 2,624
7
votes
1
answer
306
views
Does a tight apartness relation on a subobject classifier imply the elementary topos is Bool...
Given a set $S$, a tight apartness relation on $S$ is a relation $\#$ which is tight, irreflexive, symmetric, and weakly linear, or more specifically, a relation $\#$ such that
for all elements $a \i …
- 2,624
3
votes
1
answer
114
views
Analogue of Kock-Lawvere axiom for power series rings?
The Kock-Lawvere axiom for a topos $\mathcal{E}$ states that given a specified commutative ring object $R \in \mathcal{E}$, for all local Artinian $R$-algebra objects $A \in \mathcal{E}$, the morphism …
- 2,624