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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
4
votes
Is monomorphism going in both directions sufficient for isomorphism?
Dear Seamus, an example of non-isomorphic objects mutually monomorphing into each other is the following, in the category of groups ( I haven't tried to follow your sketch of construction).
Consider …
26
votes
Applications of the "other" definition of sheaves
Here is an elegant application of sheaves seen as étalé spaces.
Consider a complex manifold $M$. It automatically comes with a holomorphic local isomorphism $\pi: \mathcal O_M \to M $ described as fol …