• Corpus ID: 119146922

Grothendieck topologies on posets

  title={Grothendieck topologies on posets},
  author={Jens Hemelaer},
  journal={arXiv: Category Theory},
  • Jens Hemelaer
  • Published 25 November 2018
  • Mathematics
  • arXiv: Category Theory
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… 

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