Loogle!

Result

Found 10 declarations mentioning CategoryTheory.ShiftedHom.map.

CategoryTheory.ShiftedHom.map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2} [CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] : CategoryTheory.ShiftedHom (F.obj X) (F.obj Y) a
CategoryTheory.ShiftedHom.id_map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) : f.map (CategoryTheory.Functor.id C) = f
CategoryTheory.ShiftedHom.map_mk₀ 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2} [CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y : C} (m₀ : M) (hm₀ : m₀ = 0) (f : X ⟶ Y) (F : CategoryTheory.Functor C D) [F.CommShift M] : (CategoryTheory.ShiftedHom.mk₀ m₀ hm₀ f).map F = CategoryTheory.ShiftedHom.mk₀ m₀ hm₀ (F.map f)
CategoryTheory.ShiftedHom.comp_map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2} [CategoryTheory.Category.{v_2, u_2} D] {E : Type u_3} [CategoryTheory.Category.{v_3, u_3} E] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] [CategoryTheory.HasShift E M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] (G : CategoryTheory.Functor D E) [G.CommShift M] : f.map (F.comp G) = (f.map F).map G
CategoryTheory.ShiftedHom.map_comp 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2} [CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y Z : C} {a b c : M} (f : CategoryTheory.ShiftedHom X Y a) (g : CategoryTheory.ShiftedHom Y Z b) (h : b + a = c) (F : CategoryTheory.Functor C D) [F.CommShift M] : (f.comp g h).map F = (f.map F).comp (g.map F) h
CategoryTheory.ShiftedHom.map.eq_1 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
{C : Type u_1} [CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2} [CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] : f.map F = CategoryTheory.CategoryStruct.comp (F.map f) ((CategoryTheory.Functor.commShiftIso F a).hom.app Y)
CategoryTheory.Localization.SmallShiftedHom.equiv_mk 📋 Mathlib.CategoryTheory.Localization.SmallShiftedHom
{C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (W : CategoryTheory.MorphismProperty C) {M : Type w'} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] (L : CategoryTheory.Functor C D) [L.IsLocalization W] [L.CommShift M] {X Y : C} [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] {m : M} (f : CategoryTheory.ShiftedHom X Y m) : (CategoryTheory.Localization.SmallShiftedHom.equiv W L) (CategoryTheory.Localization.SmallShiftedHom.mk W f) = f.map L
CategoryTheory.LocalizerMorphism.smallShiftedHomMap_mk 📋 Mathlib.CategoryTheory.Localization.SmallShiftedHom
{C₁ : Type u₁} [CategoryTheory.Category.{v₁, u₁} C₁] {C₂ : Type u₂} [CategoryTheory.Category.{v₂, u₂} C₂] {W₁ : CategoryTheory.MorphismProperty C₁} {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) {M : Type w'} [AddMonoid M] [CategoryTheory.HasShift C₁ M] [CategoryTheory.HasShift C₂ M] [Φ.functor.CommShift M] {X₁ Y₁ : C₁} {X₂ Y₂ : C₂} [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₁ M X₁ Y₁] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M X₂ X₂] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M X₂ Y₂] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M Y₂ Y₂] (eX : Φ.functor.obj X₁ ≅ X₂) (eY : Φ.functor.obj Y₁ ≅ Y₂) [W₁.IsCompatibleWithShift M] [W₂.IsCompatibleWithShift M] {m : M} (f : CategoryTheory.ShiftedHom X₁ Y₁ m) : Φ.smallShiftedHomMap eX eY (CategoryTheory.Localization.SmallShiftedHom.mk W₁ f) = CategoryTheory.Localization.SmallShiftedHom.mk W₂ ((CategoryTheory.ShiftedHom.mk₀ 0 ⋯ eX.inv).comp ((f.map Φ.functor).comp (CategoryTheory.ShiftedHom.mk₀ 0 ⋯ eY.hom) ⋯) ⋯)
CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap 📋 Mathlib.CategoryTheory.Localization.SmallShiftedHom
{C₁ : Type u₁} [CategoryTheory.Category.{v₁, u₁} C₁] {C₂ : Type u₂} [CategoryTheory.Category.{v₂, u₂} C₂] {D₁ : Type u₁'} [CategoryTheory.Category.{v₁', u₁'} D₁] {D₂ : Type u₂'} [CategoryTheory.Category.{v₂', u₂'} D₂] {W₁ : CategoryTheory.MorphismProperty C₁} {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) (L₁ : CategoryTheory.Functor C₁ D₁) (L₂ : CategoryTheory.Functor C₂ D₂) [L₁.IsLocalization W₁] [L₂.IsLocalization W₂] {M : Type w'} [AddMonoid M] [CategoryTheory.HasShift C₁ M] [CategoryTheory.HasShift C₂ M] [CategoryTheory.HasShift D₁ M] [CategoryTheory.HasShift D₂ M] [L₁.CommShift M] [L₂.CommShift M] [Φ.functor.CommShift M] {X₁ Y₁ : C₁} {X₂ Y₂ : C₂} [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₁ M X₁ Y₁] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M X₂ X₂] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M X₂ Y₂] [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W₂ M Y₂ Y₂] (eX : Φ.functor.obj X₁ ≅ X₂) (eY : Φ.functor.obj Y₁ ≅ Y₂) (G : CategoryTheory.Functor D₁ D₂) [G.CommShift M] (e : Φ.functor.comp L₂ ≅ L₁.comp G) [CategoryTheory.NatTrans.CommShift e.hom M] {m : M} (f : CategoryTheory.Localization.SmallShiftedHom W₁ X₁ Y₁ m) : (CategoryTheory.Localization.SmallShiftedHom.equiv W₂ L₂) (Φ.smallShiftedHomMap eX eY f) = (CategoryTheory.ShiftedHom.mk₀ 0 ⋯ (CategoryTheory.CategoryStruct.comp (L₂.map eX.inv) (e.hom.app X₁))).comp ((((CategoryTheory.Localization.SmallShiftedHom.equiv W₁ L₁) f).map G).comp (CategoryTheory.ShiftedHom.mk₀ 0 ⋯ (CategoryTheory.CategoryStruct.comp (e.inv.app Y₁) (L₂.map eY.hom))) ⋯) ⋯
CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk 📋 Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom
{C : Type u} [CategoryTheory.Category.{v, u} C] [CategoryTheory.Abelian C] {K L : CochainComplex C ℤ} {n : ℤ} [CategoryTheory.Localization.HasSmallLocalizedShiftedHom (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) ℤ K L] [HasDerivedCategory C] (x : CochainComplex.HomComplex.Cocycle K L n) : (CategoryTheory.Localization.SmallShiftedHom.equiv (HomologicalComplex.quasiIso C (ComplexShape.up ℤ)) DerivedCategory.Q) (CochainComplex.HomComplex.CohomologyClass.mk x).toSmallShiftedHom = CategoryTheory.ShiftedHom.map (CochainComplex.HomComplex.Cocycle.equivHomShift.symm x) DerivedCategory.Q

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

By constant:
🔍 Real.sin
finds all lemmas whose statement somehow mentions the sine function.
By lemma name substring:
🔍 "differ"
finds all lemmas that have "differ" somewhere in their lemma name.
By subexpression:
🔍 _ * (_ ^ _)
finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

The pattern can also be non-linear, as in
🔍 Real.sqrt ?a * Real.sqrt ?a

If the pattern has parameters, they are matched in any order. Both of these will find List.map:
🔍 (?a -> ?b) -> List ?a -> List ?b
🔍 List ?a -> (?a -> ?b) -> List ?b
By main conclusion:
🔍 |- tsum _ = _ * tsum _
finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
🔍 |- _ < _ → tsum _ < tsum _
will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 6ff4759 serving mathlib revision edaf32c