Barycentric Subdivision and Isomorphisms of Groupoids
Sommer-Simpson, Jasha
Original · EN
Given groupoids G and H as well as an isomorphism Ψ:Sd G H between subdivisions, we construct an isomorphism P: G H. If Ψ equals Sd F for some functor F, then the constructed isomorphism P is equal to F. It follows that the restriction of Sd to the category of groupoids is conservative. These results do not hold for arbitrary categories.
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