New answers tagged topos-theory
6
votes
Categories in which isomorphism of stalks does not imply isomorphism of sheaves
Here is a reformulation/generalisation of G. Stefanich's counterexample, showing that sheaf-locality can fail very dramatically once we leave the realm of locally finitely presentable categories.
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12
votes
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Categories in which isomorphism of stalks does not imply isomorphism of sheaves
One tends to run into non-conservativity of stalks when working with sheaves of categories with colimits. There are some remarks in the literature about this point, for sheaves valued in the $\infty$-...
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