Loogle!

Result

Found 22 declarations mentioning CategoryTheory.MorphismProperty.map.

• CategoryTheory.MorphismProperty.map 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) : CategoryTheory.MorphismProperty D
• CategoryTheory.MorphismProperty.map_id_eq_isoClosure 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) : P.map (CategoryTheory.Functor.id C) = P.isoClosure
• CategoryTheory.MorphismProperty.map_id 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] (P : CategoryTheory.MorphismProperty C) [P.RespectsIso] : P.map (CategoryTheory.Functor.id C) = P
• CategoryTheory.MorphismProperty.map_respectsIso 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) : (P.map F).RespectsIso
• CategoryTheory.MorphismProperty.map_isoClosure 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) : P.isoClosure.map F = P.map F
• CategoryTheory.MorphismProperty.inverseImage_map_eq_of_isEquivalence 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) [P.RespectsIso] (F : CategoryTheory.Functor C D) [F.IsEquivalence] : (P.map F).inverseImage F = P
• CategoryTheory.MorphismProperty.map_inverseImage_eq_of_isEquivalence 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty D) [P.RespectsIso] (F : CategoryTheory.Functor C D) [F.IsEquivalence] : (P.inverseImage F).map F = P
• CategoryTheory.MorphismProperty.inverseImage_equivalence_functor_eq_map_inverse 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (Q : CategoryTheory.MorphismProperty C) [Q.RespectsIso] (E : C ≌ D) : Q.inverseImage E.inverse = Q.map E.functor
• CategoryTheory.MorphismProperty.inverseImage_equivalence_inverse_eq_map_functor 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty D) [P.RespectsIso] (E : C ≌ D) : P.inverseImage E.functor = P.map E.inverse
• CategoryTheory.MorphismProperty.map_eq_of_iso 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) {F G : CategoryTheory.Functor C D} (e : F ≅ G) : P.map F = P.map G
• CategoryTheory.MorphismProperty.map_map 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_3, u_1} D] (P : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) {E : Type u_2} [CategoryTheory.Category.{u_4, u_2} E] (G : CategoryTheory.Functor D E) : (P.map F).map G = P.map (F.comp G)
• CategoryTheory.MorphismProperty.map_inverseImage_le 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty D) (F : CategoryTheory.Functor C D) : (P.inverseImage F).map F ≤ P.isoClosure
• CategoryTheory.MorphismProperty.monotone_map 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (F : CategoryTheory.Functor C D) : Monotone fun x => x.map F
• CategoryTheory.MorphismProperty.map_le_iff 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) {F : CategoryTheory.Functor C D} (Q : CategoryTheory.MorphismProperty D) [Q.RespectsIso] : P.map F ≤ Q ↔ P ≤ Q.inverseImage F
• CategoryTheory.MorphismProperty.map_mem_map 📋 Mathlib.CategoryTheory.MorphismProperty.Basic
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u_1} [CategoryTheory.Category.{u_2, u_1} D] (P : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y) (hf : P f) : P.map F (F.map f)
• CategoryTheory.MorphismProperty.IsInvertedBy.map_iff 📋 Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
  {C₁ : Type u_1} {C₂ : Type u_2} {C₃ : Type u_3} [CategoryTheory.Category.{u_4, u_1} C₁] [CategoryTheory.Category.{u_5, u_2} C₂] [CategoryTheory.Category.{u_6, u_3} C₃] (W : CategoryTheory.MorphismProperty C₁) (F : CategoryTheory.Functor C₁ C₂) (G : CategoryTheory.Functor C₂ C₃) : (W.map F).IsInvertedBy G ↔ W.IsInvertedBy (F.comp G)
• CategoryTheory.MorphismProperty.IsInvertedBy.iff_map_le_isomorphisms 📋 Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy
  {C : Type u} [CategoryTheory.Category.{v, u} C] {D : Type u'} [CategoryTheory.Category.{v', u'} D] (W : CategoryTheory.MorphismProperty C) (F : CategoryTheory.Functor C D) : W.IsInvertedBy F ↔ W.map F ≤ CategoryTheory.MorphismProperty.isomorphisms D
• CategoryTheory.LocalizerMorphism.IsLocalizedEquivalence.of_equivalence 📋 Mathlib.CategoryTheory.Localization.LocalizerMorphism
  {C₁ : Type u₁} {C₂ : Type u₂} [CategoryTheory.Category.{v₁, u₁} C₁] [CategoryTheory.Category.{v₂, u₂} C₂] {W₁ : CategoryTheory.MorphismProperty C₁} {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) [Φ.functor.IsEquivalence] (h : W₂ ≤ W₁.map Φ.functor) : Φ.IsLocalizedEquivalence
• CategoryTheory.Functor.IsLocalization.of_comp 📋 Mathlib.CategoryTheory.Localization.Composition
  {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [CategoryTheory.Category.{v₁, u₁} C₁] [CategoryTheory.Category.{v₂, u₂} C₂] [CategoryTheory.Category.{v₃, u₃} C₃] (L₁ : CategoryTheory.Functor C₁ C₂) (L₂ : CategoryTheory.Functor C₂ C₃) (W₁ : CategoryTheory.MorphismProperty C₁) (W₂ : CategoryTheory.MorphismProperty C₂) (W₃ : CategoryTheory.MorphismProperty C₁) [L₁.IsLocalization W₁] [(L₁.comp L₂).IsLocalization W₃] (hW₁₃ : W₁ ≤ W₃) (hW₂₃ : W₂ = W₃.map L₁) : L₂.IsLocalization W₂
• CategoryTheory.Functor.IsLocalization.comp 📋 Mathlib.CategoryTheory.Localization.Composition
  {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [CategoryTheory.Category.{v₁, u₁} C₁] [CategoryTheory.Category.{v₂, u₂} C₂] [CategoryTheory.Category.{v₃, u₃} C₃] (L₁ : CategoryTheory.Functor C₁ C₂) (L₂ : CategoryTheory.Functor C₂ C₃) (W₁ : CategoryTheory.MorphismProperty C₁) (W₂ : CategoryTheory.MorphismProperty C₂) [L₁.IsLocalization W₁] [L₂.IsLocalization W₂] (W₃ : CategoryTheory.MorphismProperty C₁) (hW₃ : W₃.IsInvertedBy (L₁.comp L₂)) (hW₁₃ : W₁ ≤ W₃) (hW₂₃ : W₂ ≤ W₃.map L₁) : (L₁.comp L₂).IsLocalization W₃
• CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.comp 📋 Mathlib.CategoryTheory.Localization.Composition
  {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} {E : Type u₄} [CategoryTheory.Category.{v₁, u₁} C₁] [CategoryTheory.Category.{v₂, u₂} C₂] [CategoryTheory.Category.{v₃, u₃} C₃] [CategoryTheory.Category.{v₄, u₄} E] {L₁ : CategoryTheory.Functor C₁ C₂} {L₂ : CategoryTheory.Functor C₂ C₃} {W₁ : CategoryTheory.MorphismProperty C₁} {W₂ : CategoryTheory.MorphismProperty C₂} (h₁ : CategoryTheory.Localization.StrictUniversalPropertyFixedTarget L₁ W₁ E) (h₂ : CategoryTheory.Localization.StrictUniversalPropertyFixedTarget L₂ W₂ E) (W₃ : CategoryTheory.MorphismProperty C₁) (hW₃ : W₃.IsInvertedBy (L₁.comp L₂)) (hW₁₃ : W₁ ≤ W₃) (hW₂₃ : W₂ ≤ W₃.map L₁) : CategoryTheory.Localization.StrictUniversalPropertyFixedTarget (L₁.comp L₂) W₃ E
• HomotopyCategory.quasiIso_eq_quasiIso_map_quotient 📋 Mathlib.Algebra.Homology.Localization
  (C : Type u_1) [CategoryTheory.Category.{u_3, u_1} C] {ι : Type u_2} (c : ComplexShape ι) [CategoryTheory.Preadditive C] [CategoryTheory.CategoryWithHomology C] : HomotopyCategory.quasiIso C c = (HomologicalComplex.quasiIso C c).map (HomotopyCategory.quotient C c)

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:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. 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

4. 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 19971e9 serving mathlib revision 40fea08