refactor(CategoryTheory/Limits): use compEvaluation in limitIsoFlipCompLim - #43568
refactor(CategoryTheory/Limits): use compEvaluation in limitIsoFlipCompLim#43568kim-em wants to merge 1 commit into
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PR summary 12df66b4a1Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…mpLim limitIsoFlipCompLim and colimitIsoFlipCompColim identified F ⋙ (evaluation K C).obj k with F.flip.obj k by unfolding; insert HasLimit.isoOfNatIso (compEvaluation F k) instead. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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| @[simps!] | ||
| def limitIsoFlipCompLim [HasLimitsOfShape J C] (F : J ⥤ K ⥤ C) : limit F ≅ F.flip ⋙ lim := | ||
| NatIso.ofComponents (limitObjIsoLimitCompEvaluation F) | ||
| NatIso.ofComponents (fun k => |
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This proof uses Functor.comp_map. Then, I do not understand why not just doing the following because cat_disch (just a combination of intros, ext, simp) proves the goal:
NatIso.ofComponents (fun k =>
limitObjIsoLimitCompEvaluation F k ≪≫ HasLimit.isoOfNatIso (compEvaluation F k))
This PR inserts
HasLimit.isoOfNatIso (compEvaluation F k)into the components oflimitIsoFlipCompLimandcolimitIsoFlipCompColim, which currently identifyF ⋙ (evaluation K C).obj kwithF.flip.obj kby unfolding, and adapts the two proofs (colimitLimitToLimitColimitConeandyonedaYonedaColimit_app_inv) that relied on that unfolding.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); the associator and unitor fixes are in #43566.🤖 Prepared with Claude Code