On a formula that is not in "Grothendieck Topologies in Posets"

2021/07/18 by Ochs, Eduardo
#Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.08501

Abstract

The paper "Grothendieck Topologies on Posets" by A.J. Lindenhovius shows that when P is an Artinian poset and E is the topos Set^P then there are bijections between the set of subsets of P, the set of Grothendieck topologies on E, and the set of nuclei on the Heyting Algebra Sub(1_E). It also shows that there are nice formulas for converting between subsets, Grothendieck topologies, and nuclei, but the formula for converting a nucleus to a subset is not spelled out explicitly. These notes fix that gap.

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