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Mathlib.lean

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@@ -3452,6 +3452,7 @@ public import Mathlib.Combinatorics.Enumerative.Stirling
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public import Mathlib.Combinatorics.Extremal.RuzsaSzemeredi
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public import Mathlib.Combinatorics.Graph.Basic
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public import Mathlib.Combinatorics.Graph.Delete
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public import Mathlib.Combinatorics.Graph.Lattice
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public import Mathlib.Combinatorics.Graph.Subgraph
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public import Mathlib.Combinatorics.HalesJewett
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public import Mathlib.Combinatorics.Hall.Basic

Mathlib/Algebra/Category/Grp/AB.lean

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@@ -15,7 +15,7 @@ public import Mathlib.CategoryTheory.Limits.FunctorCategory.EpiMono
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# AB axioms for the category of abelian groups
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This file proves that the category of abelian groups satisfies Grothendieck's axioms AB5, AB4, and
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AB4*.
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AB4\*.
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-/
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@[expose] public section

Mathlib/Algebra/Category/ModuleCat/AB.lean

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@@ -14,7 +14,7 @@ public import Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic
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# AB axioms in module categories
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This file proves that the category of modules over a ring satisfies Grothendieck's axioms AB5, AB4,
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and AB4*. Further, it proves that `R` is a separator in the category of modules over `R`, and
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and AB4\*. Further, it proves that `R` is a separator in the category of modules over `R`, and
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concludes that this category is Grothendieck abelian.
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-/
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Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean

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@@ -82,7 +82,6 @@ def freeHomEquiv {X : Type u} {M : ModuleCat.{u} R} :
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variable (R)
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set_option backward.isDefEq.respectTransparency false in
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/-- The free-forgetful adjunction for R-modules.
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-/
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def adj : free R ⊣ forget (ModuleCat.{u} R) :=

Mathlib/Algebra/Category/ModuleCat/EpiMono.lean

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@@ -61,13 +61,11 @@ instance mono_as_hom'_subtype (U : Submodule R X) : Mono (ModuleCat.ofHom U.subt
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instance epi_as_hom''_mkQ (U : Submodule R X) : Epi (ModuleCat.ofHom U.mkQ) :=
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(epi_iff_range_eq_top _).mpr <| Submodule.range_mkQ _
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set_option backward.isDefEq.respectTransparency false in
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instance forget_preservesEpimorphisms : (forget (ModuleCat.{v} R)).PreservesEpimorphisms where
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preserves f hf := by
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rw [CategoryTheory.ofHom_epi_iff_surjective, ← epi_iff_surjective]
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exact hf
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set_option backward.isDefEq.respectTransparency false in
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instance forget_preservesMonomorphisms : (forget (ModuleCat.{v} R)).PreservesMonomorphisms where
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preserves f hf := by
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rw [CategoryTheory.ofHom_mono_iff_injective, ← mono_iff_injective]

Mathlib/Algebra/Category/ModuleCat/Presheaf/Generator.lean

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@@ -167,7 +167,6 @@ lemma ι_fromFreeYonedaCoproduct_apply (m : M.Elements) (X : Cᵒᵖ) (x : m.fre
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ConcreteCategory.congr_hom
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((evaluation R X ⋙ forget _).congr_map (M.ι_fromFreeYonedaCoproduct m)) x
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set_option backward.isDefEq.respectTransparency false in
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@[simp]
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lemma fromFreeYonedaCoproduct_app_mk (m : M.Elements) :
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M.fromFreeYonedaCoproduct.app _ (M.freeYonedaCoproductMk m) = m.2 := by

Mathlib/Algebra/Category/Ring/FinitePresentation.lean

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@@ -137,7 +137,6 @@ lemma RingHom.EssFiniteType.exists_eq_comp_ι_app_of_isColimit (hf : f.hom.Finit
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rw [c.w, hg']
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rfl
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set_option backward.isDefEq.respectTransparency false in
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/-- If `S` is a finitely presented `R`-algebra, then `Hom_R(S, -)` preserves filtered colimits. -/
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lemma CommRingCat.preservesColimit_coyoneda_of_finitePresentation
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(S : Under R) (hS : S.hom.hom.FinitePresentation) (F : J ⥤ Under R)

Mathlib/Algebra/Category/Ring/Under/Basic.lean

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instance (A : Under R) : Algebra R A := RingHom.toAlgebra A.hom.hom
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set_option backward.isDefEq.respectTransparency false in
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/-- Turn a morphism in `Under R` into an algebra homomorphism. -/
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def toAlgHom {A B : Under R} (f : A ⟶ B) : A →ₐ[R] B where
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__ := f.right.hom

Mathlib/Algebra/DualNumber.lean

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@@ -223,7 +223,7 @@ theorem range_lift
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AlgHom.map_adjoin, ← AlgHom.range_comp, Set.image_singleton, lift_apply_eps, lift_comp_inlHom,
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Algebra.map_top]
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/-- Show DualNumber with values x and y as an "x + y*ε" string -/
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/-- Show DualNumber with values x and y as an `"x + y*ε"` string -/
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instance instRepr [Repr R] : Repr (DualNumber R) where
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reprPrec f p :=
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(if p > 65 then (Std.Format.bracket "(" · ")") else (·)) <|

Mathlib/Algebra/FiniteSupport/Basic.lean

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@@ -13,7 +13,7 @@ public import Mathlib.Data.Set.Finite.Lattice
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import Mathlib.Algebra.Group.Support
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/-!
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# Make fun_prop work for finite (multiplicative) support
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# Make `fun_prop` work for finite (multiplicative) support
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We provide API lemmas for the predicate `HasFiniteMulSupport` (and its additivized version
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`HasFiniteSupport`) on functions so that `fun_prop` can prove it for functions that are

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