Loogle!

Result

Found 13 declarations mentioning CategoryTheory.MorphismProperty.RightFraction.map.

• CategoryTheory.MorphismProperty.RightFraction.map 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.RightFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : L.obj X ⟶ L.obj Y
• CategoryTheory.MorphismProperty.RightFraction.map_ofHom 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (W : CategoryTheory.MorphismProperty C) {X Y : C} (f : X ⟶ Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) [W.ContainsIdentities] : (CategoryTheory.MorphismProperty.RightFraction.ofHom W f).map L hL = L.map f
• CategoryTheory.MorphismProperty.RightFraction.map_eq_iff 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasRightCalculusOfFractions] {X Y : C} (φ ψ : W.RightFraction X Y) : φ.map L ⋯ = ψ.map L ⋯ ↔ CategoryTheory.MorphismProperty.RightFractionRel φ ψ
• CategoryTheory.Localization.exists_rightFraction 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_4, u_1} C] [CategoryTheory.Category.{u_3, u_2} D] (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasRightCalculusOfFractions] {X Y : C} (f : L.obj X ⟶ L.obj Y) : ∃ φ, f = φ.map L ⋯
• CategoryTheory.MorphismProperty.LeftFraction.op_map 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.LeftFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : (φ.map L hL).op = φ.op.map L.op ⋯
• CategoryTheory.MorphismProperty.RightFraction.op_map 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.RightFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : (φ.map L hL).op = φ.op.map L.op ⋯
• CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (W : CategoryTheory.MorphismProperty C) {X Y : C} (s : Y ⟶ X) (hs : W s) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : CategoryTheory.CategoryStruct.comp (L.map s) ((CategoryTheory.MorphismProperty.RightFraction.ofInv s hs).map L hL) = CategoryTheory.CategoryStruct.id (L.obj Y)
• CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (W : CategoryTheory.MorphismProperty C) {X Y : C} (s : Y ⟶ X) (hs : W s) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.RightFraction.ofInv s hs).map L hL) (L.map s) = CategoryTheory.CategoryStruct.id (L.obj X)
• CategoryTheory.MorphismProperty.RightFraction.map_hom_ofInv_id_assoc 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (W : CategoryTheory.MorphismProperty C) {X Y : C} (s : Y ⟶ X) (hs : W s) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) {Z : D} (h : L.obj Y ⟶ Z) : CategoryTheory.CategoryStruct.comp (L.map s) (CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.RightFraction.ofInv s hs).map L hL) h) = h
• CategoryTheory.MorphismProperty.RightFraction.map_ofInv_hom_id_assoc 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] (W : CategoryTheory.MorphismProperty C) {X Y : C} (s : Y ⟶ X) (hs : W s) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) {Z : D} (h : L.obj X ⟶ Z) : CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.RightFraction.ofInv s hs).map L hL) (CategoryTheory.CategoryStruct.comp (L.map s) h) = h
• CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.RightFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : CategoryTheory.CategoryStruct.comp (L.map φ.s) (φ.map L hL) = L.map φ.f
• CategoryTheory.MorphismProperty.RightFraction.map.eq_1 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.RightFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : φ.map L hL = CategoryTheory.CategoryStruct.comp (CategoryTheory.inv (L.map φ.s)) (L.map φ.f)
• CategoryTheory.MorphismProperty.RightFraction.map_s_comp_map_assoc 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
  {C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.RightFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) {Z : D} (h : L.obj Y ⟶ Z) : CategoryTheory.CategoryStruct.comp (L.map φ.s) (CategoryTheory.CategoryStruct.comp (φ.map L hL) h) = CategoryTheory.CategoryStruct.comp (L.map φ.f) h

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