@@ -392,6 +392,7 @@ namespace SubobjectRepresentableBy
392392given `h : SubobjectRepresentableBy Ω`. -/
393393def Ω₀ : Subobject Ω := h.homEquiv (𝟙 Ω)
394394
395+ set_option linter.dupNamespace false in
395396@ [deprecated (since := "2026-03-06" )]
396397alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.Ω₀ := Ω₀
397398@ [deprecated (since := "2026-03-06" )]
@@ -403,6 +404,7 @@ lemma homEquiv_eq {X : C} (f : X ⟶ Ω) :
403404 h.homEquiv f = (Subobject.pullback f).obj h.Ω₀ := by
404405 simpa using ! h.homEquiv_comp f (𝟙 _)
405406
407+ set_option linter.dupNamespace false in
406408@ [deprecated (since := "2026-03-06" )]
407409alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq := homEquiv_eq
408410@ [deprecated (since := "2026-03-06" )]
@@ -414,6 +416,7 @@ lemma pullback_homEquiv_symm_obj_Ω₀ {X : C} (x : Subobject X) :
414416 (Subobject.pullback (h.homEquiv.symm x)).obj h.Ω₀ = x := by
415417 rw [← homEquiv_eq, Equiv.apply_symm_apply]
416418
419+ set_option linter.dupNamespace false in
417420@ [deprecated (since := "2026-03-06" )]
418421alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀ :=
419422 pullback_homEquiv_symm_obj_Ω₀
@@ -428,6 +431,7 @@ variable {U X : C} (m : U ⟶ X) [Mono m]
428431/-- `h.χ m` is the characteristic map of monomorphism `m` given by the bijection `h.homEquiv`. -/
429432def χ : X ⟶ Ω := h.homEquiv.symm (Subobject.mk m)
430433
434+ set_option linter.dupNamespace false in
431435@ [deprecated (since := "2026-03-06" )]
432436alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.χ := χ
433437@ [deprecated (since := "2026-03-06" )]
@@ -440,6 +444,7 @@ noncomputable def iso : MonoOver.mk m ≅
440444 (Subobject.representativeIso (.mk m)).symm ≪≫ Subobject.representative.mapIso
441445 (eqToIso (h.pullback_homEquiv_symm_obj_Ω₀ (.mk m)).symm)
442446
447+ set_option linter.dupNamespace false in
443448@ [deprecated (since := "2026-03-06" )]
444449alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.iso := iso
445450@ [deprecated (since := "2026-03-06" )]
@@ -459,6 +464,7 @@ alias _root_.CategoryTheory.Classifier.SubobjectRepresentableBy.iso := iso
459464noncomputable def π : U ⟶ Subobject.underlying.obj h.Ω₀ :=
460465 (h.iso m).hom.hom.left ≫ Subobject.pullbackπ (h.χ m) h.Ω₀
461466
467+ set_option linter.dupNamespace false in
462468@ [deprecated (since := "2026-03-06" )]
463469alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.π := π
464470@ [deprecated (since := "2026-03-06" )]
@@ -473,6 +479,7 @@ lemma iso_inv_left_π :
473479 convert! Category.id_comp _ using 2
474480 exact (MonoOver.forget _ ⋙ Over.forget _).congr_map (h.iso m).inv_hom_id
475481
482+ set_option linter.dupNamespace false in
476483@ [deprecated (since := "2026-03-06" )]
477484alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_π := iso_inv_left_π
478485@ [deprecated (since := "2026-03-06" )]
@@ -484,13 +491,15 @@ lemma iso_inv_hom_left_comp :
484491 ((Subobject.pullback (h.χ m)).obj h.Ω₀).arrow :=
485492 MonoOver.w (h.iso m).inv
486493
494+ set_option linter.dupNamespace false in
487495@ [deprecated (since := "2026-03-06" )]
488496alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp :=
489497 iso_inv_hom_left_comp
490498@ [deprecated (since := "2026-03-06" )]
491499alias _root_.CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_hom_left_comp :=
492500 iso_inv_hom_left_comp
493501
502+ set_option linter.dupNamespace false in
494503@ [deprecated (since := "2025-12-18" )]
495504alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.iso_inv_left_comp :=
496505 iso_inv_hom_left_comp
@@ -503,6 +512,7 @@ lemma isPullback {U X : C} (m : U ⟶ X) [Mono m] :
503512 (Iso.refl _) (Iso.refl _)
504513 all_goals simp [MonoOver.forget]
505514
515+ set_option linter.dupNamespace false in
506516@ [deprecated (since := "2026-03-06" )]
507517alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.isPullback := isPullback
508518@ [deprecated (since := "2026-03-06" )]
@@ -515,6 +525,7 @@ lemma uniq {χ' : X ⟶ Ω} {π : U ⟶ h.Ω₀}
515525 simp only [χ, Equiv.apply_symm_apply, homEquiv_eq]
516526 simpa using ! Subobject.pullback_obj_mk sq.flip
517527
528+ set_option linter.dupNamespace false in
518529@ [deprecated (since := "2026-03-06" )]
519530alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.uniq := uniq
520531@ [deprecated (since := "2026-03-06" )]
@@ -532,6 +543,7 @@ noncomputable def isTerminalΩ₀ : IsTerminal (h.Ω₀ : C) :=
532543 rw [← cancel_mono h.Ω₀.arrow, h.uniq this,
533544 ← (h.isPullback (𝟙 X)).w, Category.id_comp])
534545
546+ set_option linter.dupNamespace false in
535547@ [deprecated (since := "2026-03-06" )]
536548alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.isTerminalΩ₀ := isTerminalΩ₀
537549@ [deprecated (since := "2026-03-06" )]
@@ -540,6 +552,7 @@ alias _root_.CategoryTheory.Classifier.SubobjectRepresentableBy.isTerminalΩ₀
540552/-- The unique map to the terminal object. -/
541553noncomputable def χ₀ (U : C) : U ⟶ h.Ω₀ := h.isTerminalΩ₀.from U
542554
555+ set_option linter.dupNamespace false in
543556@ [deprecated (since := "2026-03-06" )]
544557alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.χ₀ := χ₀
545558@ [deprecated (since := "2026-03-06" )]
@@ -548,6 +561,7 @@ alias _root_.CategoryTheory.Classifier.SubobjectRepresentableBy.χ₀ := χ₀
548561include h in
549562lemma hasTerminal : HasTerminal C := h.isTerminalΩ₀.hasTerminal
550563
564+ set_option linter.dupNamespace false in
551565@ [deprecated (since := "2026-03-06" )]
552566alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.hasTerminal := hasTerminal
553567@ [deprecated (since := "2026-03-06" )]
@@ -559,6 +573,7 @@ variable [HasTerminal C]
559573noncomputable def isoΩ₀ : (h.Ω₀ : C) ≅ ⊤_ C :=
560574 h.isTerminalΩ₀.conePointUniqueUpToIso (limit.isLimit _)
561575
576+ set_option linter.dupNamespace false in
562577@ [deprecated (since := "2026-03-06" )]
563578alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.isoΩ₀ := isoΩ₀
564579@ [deprecated (since := "2026-03-06" )]
@@ -582,6 +597,7 @@ noncomputable def classifier : Subobject.Classifier C where
582597 (by simp) (h.isTerminalΩ₀.hom_ext _ _) (by simp) (by simp)
583598 exact h.uniq this
584599
600+ set_option linter.dupNamespace false in
585601@ [deprecated (since := "2026-03-06" )]
586602alias _root.CategoryTheory.Classifier.SubobjectRepresentableBy.classifier := classifier
587603@ [deprecated (since := "2026-03-06" )]
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