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

Abstract

The paper "Grothendieck Topologies on Posets" by A.J. Lindenhovius shows that when $\mathbf{P}$ is an Artinian poset and $\mathbf{E}$ is the topos ${\mathbf{Set}}^{\mathbf{P}}$ then there are bijections between the set of subsets of $\mathbf{P}$, the set of Grothendieck topologies on $\mathbf{E}$, and the set of nuclei on the Heyting Algebra $\mathrm{Sub}(1_{\mathbf{E}})$. 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.

4 pages

References in corpus (1)

• Grothendieck topologies on a poset

Cited by in corpus (1)

• Each closure operator induces a topology and vice-versa ("version for children")