refactor(AlgebraicGeometry/Modules): transport pushforward along Opens.map functoriality isos - #43570
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refactor(AlgebraicGeometry/Modules): transport pushforward along Opens.map functoriality isos#43570kim-em wants to merge 2 commits into
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PR summary 0ca56e655aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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| Current number | Change | Type (strong) |
|---|---|---|
| backward.isDefEq.respectTransparency | 4684 | -3 |
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…functor bracketings Introduce pushforwardIdHom and pushforwardCompHom as the honestly-typed data along which the pushforward by the identity and by a composition are taken (they are the unitor and associator composed with Functor.opId/opComp), and transport the associativity and unitality isomorphisms of pushforward and pullback along the functor associator and unitors instead of relying on the two bracketings being definitionally equal. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
…s.map functoriality isos Define Scheme.Modules.pushforwardId and pushforwardComp by transporting along the new opensMapIdIso and opensMapCompIso instead of identifying Opens.map (𝟙 X).base with the identity and Opens.map (f ≫ g).base with the composition by unfolding. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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This PR defines
Scheme.Modules.pushforwardIdandpushforwardCompby transporting the sheaf-of-modules isomorphisms along the existingOpens.mapIdandOpens.mapComp(viaSheafOfModules.pushforwardCongr₂) rather than by identifyingOpens.map (𝟙 X).basewith𝟭andOpens.map (f ≫ g).basewithOpens.map g.base ⋙ Opens.map f.baseby unfoldingOpens.map. The componentwise simp lemmas becomeM.presheaf.map_idrather thanrfl, and the pseudofunctor coherence fields are discharged explicitly sincecat_dischno longer finds them by reflexivity. Also adds the simp lemmaAdj.eqToHom_τl.It is extracted from Paul Reichert's experiment making
Functor.compandFunctor.idinstance_reducible(master...leanprover-community:mathlib4-nightly-testing:datokrat/functorcomp, discussed at https://leanprover.zulipchat.com/#narrow/channel/113488-general/topic/backward.2EisDefEq.2ErespectTransparency), and depends on #43569. The diff relative to that PR is kim-em/mathlib4@associators-sheaves...opens-map.🤖 Prepared with Claude Code