Grothendieck topologies on posets
Jens Hemelaer

TL;DR
This paper extends the classification of Grothendieck topologies on posets beyond Artinian cases, providing explicit descriptions and cardinalities for various families, by translating locale and domain theory results.
Contribution
It generalizes Lindenhovius's classification to broader posets using locale and domain theory, offering explicit descriptions and cardinality computations.
Findings
Explicit descriptions of Grothendieck topologies with enough points
Cardinality calculations for various poset examples
Extension of classification beyond Artinian posets
Abstract
Lindenhovius has studied Grothendieck topologies on posets and has given a complete classification in the case that the poset is Artinian. We extend his approach to more general posets, by translating known results in locale and domain theory to the study of Grothendieck topologies. In particular, explicit descriptions are given for the family of Grothendieck topologies with enough points and the family of Grothendieck topologies of finite type. As an application, we compute the cardinalities of these families in various examples.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Homotopy and Cohomology in Algebraic Topology
