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[Merged by Bors] - fix(CategoryTheory/MorphismProperty/Limits): change duplicate lemma #39647

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[Merged by Bors] - fix(CategoryTheory/MorphismProperty/Limits): change duplicate lemma #39647

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9860e46
fix: change incorrectly named lemma
robin-carlier May 21, 2026
ba0f3f7
fix: fix docstrings
robin-carlier May 21, 2026
cd9b813
fix: fix docstrings again
robin-carlier May 21, 2026
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16 changes: 8 additions & 8 deletions Mathlib/CategoryTheory/MorphismProperty/Limits.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -1012,10 +1012,10 @@ instance (P : MorphismProperty C) [P.HasPullbacks] (P' : MorphismProperty C) :

lemma hasPullbacksAgainst_top_iff
(P : MorphismProperty C) :
P.IsStableUnderBaseChangeAgainst ⊤ ↔ P.IsStableUnderBaseChange where
P.HasPullbacksAgainst ⊤ ↔ P.HasPullbacks where
mp h :=
⟨fun {_ _ _ _} _ _ _ _ h' h'' ↦
(h.isStableUnderBaseChangeAlong _ (by tauto)).of_isPullback h' h''⟩
⟨fun _ h' ↦
(h.hasPullbacksAlong _ (by tauto)).hasPullback _ h'⟩
mpr _ := inferInstance

lemma _root_.CategoryTheory.Limits.hasPullback_ofHasPullbacksAgainst
Expand All @@ -1027,7 +1027,7 @@ lemma _root_.CategoryTheory.Limits.hasPullback_ofHasPullbacksAgainst
MorphismProperty.HasPullbacksAlong.hasPullback f hf

/-- `P.IsStableUnderCobaseChangeAgainst P'` states that for any morphism `f` satisfying `P` and
any morphism `g` with the same codomain as `f` satisfying `P'`, any pullback of `f` along `g`
any morphism `g` with the same domain as `f` satisfying `P'`, any pushout of `f` along `g`
also satisfies `P`. -/
class IsStableUnderCobaseChangeAgainst
(P P' : MorphismProperty C) : Prop where
Expand All @@ -1047,7 +1047,7 @@ lemma isStableUnderCobaseChangeAgainst_top_iff
(h.isStableUnderCobaseChangeAlong _ (by tauto)).of_isPushout h' h''⟩
mpr _ := inferInstance

/-- `P.HasPullbacksAgainst P'` states that for any morphism `f` satisfying `P'`,
/-- `P.HasPushoutsAgainst P'` states that for any morphism `f` satisfying `P'`,
`P` has pushouts along `f`. -/
class HasPushoutsAgainst
(P P' : MorphismProperty C) : Prop where
Expand All @@ -1060,10 +1060,10 @@ instance (P : MorphismProperty C) [P.HasPushouts] (P' : MorphismProperty C) :

lemma hasPushoutsAgainst_top_iff
(P : MorphismProperty C) :
P.IsStableUnderCobaseChangeAgainst ⊤ ↔ P.IsStableUnderCobaseChange where
P.HasPushoutsAgainst ⊤ ↔ P.HasPushouts where
mp h :=
⟨fun {_ _ _ _} _ _ _ _ h' h'' ↦
(h.isStableUnderCobaseChangeAlong _ (by tauto)).of_isPushout h' h''⟩
⟨fun _ h' ↦
(h.hasPushoutsAlong _ (by tauto)).hasPushout _ h'⟩
mpr _ := inferInstance

lemma _root_.CategoryTheory.Limits.hasPushout_ofHasPushoutsAgainst
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