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Grothendieck Topologies on a Poset by Lindenhovius, Bert is a scholarly article available to read on EtoBox.

What is Grothendieck Topologies on a Poset about?

We investigate Grothendieck topologies (in the sense of sheaf theory) on a poset $\P$ that are generated by some subset of $\P$. We show that such Grothendieck topologies exhaust all possibilities if and only if $\P$ is Artinian. If $\P$ is not Artinian, other families of Grothendieck topologies on $\P$ exist that are not generated by some subset of $\P$, but even those are related to the Grothendieck topologies generated by subsets. Furthermore, we investigate several notions of equivalences of Grothendieck topologies, and using a posetal version of the Comparison Lemma, a sheaf-theoretic result known as the Comparison Lemma, going back to Grothendieck et al \cite{SGA4}, we calculate the sheaves with respect to most of the Grothendieck topologies we have found.

Author

Lindenhovius, Bert

Published

2014

Language

EN