[Merged by Bors] - feat(CategoryTheory/Sites): discrete sheaves#13947
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[Merged by Bors] - feat(CategoryTheory/Sites): discrete sheaves#13947dagurtomas wants to merge 17 commits intomasterfrom
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PR summary ad6c09d123Import changesNo significant changes to the import graph
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dagurtomas
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This PR defines the property of discreteness for sheaves. A discrete sheaf in this context is a sheaf `F` such that the counit `(F(*))^cst ⟶ F` is an isomorphism. Here `*` denotes a particular chosen terminal object of the defining site, and `cst` denotes the constant sheaf. We also prove that this property is invariant under equivalence of categories and that certain well-behaved "forgetful" functors preserve and reflect the property.
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This PR defines the property of discreteness for sheaves. A discrete sheaf in this context is a sheaf `F` such that the counit `(F(*))^cst ⟶ F` is an isomorphism. Here `*` denotes a particular chosen terminal object of the defining site, and `cst` denotes the constant sheaf. We also prove that this property is invariant under equivalence of categories and that certain well-behaved "forgetful" functors preserve and reflect the property.
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mathlib-bors bot
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This PR defines the property of discreteness for sheaves. A discrete sheaf in this context is a sheaf `F` such that the counit `(F(*))^cst ⟶ F` is an isomorphism. Here `*` denotes a particular chosen terminal object of the defining site, and `cst` denotes the constant sheaf. We also prove that this property is invariant under equivalence of categories and that certain well-behaved "forgetful" functors preserve and reflect the property.
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This PR defines the property of discreteness for sheaves. A discrete sheaf in this context is a sheaf `F` such that the counit `(F(*))^cst ⟶ F` is an isomorphism. Here `*` denotes a particular chosen terminal object of the defining site, and `cst` denotes the constant sheaf. We also prove that this property is invariant under equivalence of categories and that certain well-behaved "forgetful" functors preserve and reflect the property.
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This PR defines the property of discreteness for sheaves. A discrete sheaf in this context is a sheaf
Fsuch that the counit(F(*))^cst ⟶ Fis an isomorphism. Here*denotes a particular chosen terminal object of the defining site, andcstdenotes the constant sheaf.We also prove that this property is invariant under equivalence of categories and that certain well-behaved "forgetful" functors preserve and reflect the property.
This will be used in a future PR (#14027) to characterise discrete (light) condensed sets and modules.
The two lemmas
sheafComposeNatIso_app_counitandconstantCommuteComposeApp_comp_counitadded here are not used in this PR, but will be useful in the characterisation of discrete condensed modules.