A Topological Groupoid Representing the Topos of Presheaves on a Monoid
Copyright policy )A Topological Groupoid Representing the Topos of Presheaves on a Monoid
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 topos.
23 pages
- University of Antwerp Belgium
Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Mathematics - Category Theory, Category Theory (math.CT), Number Theory (math.NT), Algebraic Geometry (math.AG), Mathematics
Mathematics - Algebraic Geometry, Mathematics - Number Theory, FOS: Mathematics, Mathematics - Category Theory, Category Theory (math.CT), Number Theory (math.NT), Algebraic Geometry (math.AG), Mathematics
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