A Topological Groupoid Representing the Topos of Presheaves on a Monoid

@article{Hemelaer2020ATG,
  title={A Topological Groupoid Representing the Topos of Presheaves on a Monoid},
  author={Jens Hemelaer},
  journal={Applied Categorical Structures},
  year={2020},
  pages={1-24}
}
  • Jens Hemelaer
  • Published 2020
  • Mathematics, Computer Science
  • Applied Categorical Structures
Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos of presheaves on an arbitrary monoid. If the monoid is embeddable in a group, the resulting topological groupoid is the action groupoid for a discrete group acting on a topological space. For these monoids, we show how to compute the points of the associated… Expand
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