feat(CategoryTheory/Sites): the fiber functor associated to Point.comap#35722
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joelriou wants to merge 7 commits intoleanprover-community:masterfrom
Open
feat(CategoryTheory/Sites): the fiber functor associated to Point.comap#35722joelriou wants to merge 7 commits intoleanprover-community:masterfrom
Point.comap#35722joelriou wants to merge 7 commits intoleanprover-community:masterfrom
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PR summary 360d94e7b3Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Point.comapPoint.comap
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This PR/issue depends on:
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The definition
Point.comapis moved to a separate file. Using results on skyscraper sheaves, we obtain that ifF : C ⥤ Dis a representably flat continuous functor between sites(C, J)and(D, K),Φis a point of(D, K), then the fiber functor attached to the pointΦ.comap F hFof the site(C, J)(wherehF : CoverPreserving J K F) identifies to the composition of the pullback functor forFfollowed by the fiber functor attached to the pointΦ. This is a generalization to arbitrary sites of https://leanprover-community.github.io/mathlib4_docs/Mathlib/Topology/Sheaves/Stalks.html#TopCat.Presheaf.stalkPullbackIsoCo-authored-by: Christian Merten