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For questions about sheaves on a topological space.
15
votes
An apparent equivalence of the category of affine schemes over $S$ and the category of quasi...
What is true is that there is an antiequivalence between the category of schemes affine over $S$ (that is $S$-schemes for which the preimage of an open affine of $S$ is an open affine) and quasi-coher …
6
votes
Accepted
Homotopy cosheaf?
This is just a sheaf valued in the ∞-category $\mathrm{Space}^{op}$. It is usually called a cosheaf. A place where this kind of thing shows up is in factorization algebras, that can be described as pa …