https://lievenlebruyn.github.io/neverendingbooks/grothendieck-topologies-as-functors-to-top/ Sat, 31 Aug 2024 11:44:40 +0000 hourly 1 https://wordpress.org/?v=6.6.1 https://lievenlebruyn.github.io/neverendingbooks/grothendieck-topologies-as-functors-to-top/#comment-63 Wed, 02 Mar 2022 11:00:14 +0000 http://www.neverendingbooks.org/?p=6806#comment-63 No, I haven’t Tim, but in retrospect I think I’m just rephrasing here the fact that for a small category, Grothendieck topologies coincide with Lawvere-Tierney topologies. They are determined by a closure operator on the subobject classifier $\Omega$ which assigns (contravariantly) to an object $C$ the set $\Omega(C)$ of all sieves on $C$. Such a closure operator then gives a topology on every $y(C)$.

]]> https://lievenlebruyn.github.io/neverendingbooks/grothendieck-topologies-as-functors-to-top/#comment-62 Tue, 01 Mar 2022 15:42:07 +0000 http://www.neverendingbooks.org/?p=6806#comment-62 Did you ever find a reference or rebuttal for this? It’s a really nice idea!

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