Loogle!
Result
Found 26 declarations mentioning CategoryTheory.MorphismProperty.LeftFraction.map.
- CategoryTheory.MorphismProperty.LeftFraction.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) : L.obj X ⟶ L.obj Y - CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.map_mk 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
{C : Type u_1} [CategoryTheory.Category.{u_4, u_1} C] {E : Type u_3} [CategoryTheory.Category.{u_5, u_3} E] {W : CategoryTheory.MorphismProperty C} {X Y : C} (f : W.LeftFraction X Y) (F : CategoryTheory.Functor C E) (hF : W.IsInvertedBy F) : (CategoryTheory.MorphismProperty.LeftFraction.Localization.Hom.mk f).map F hF = f.map F hF - CategoryTheory.MorphismProperty.LeftFraction.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.LeftFraction.ofHom W f).map L hL = L.map f - CategoryTheory.MorphismProperty.LeftFraction.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.HasLeftCalculusOfFractions] {X Y : C} (φ ψ : W.LeftFraction X Y) : φ.map L ⋯ = ψ.map L ⋯ ↔ CategoryTheory.MorphismProperty.LeftFractionRel φ ψ - CategoryTheory.Localization.exists_leftFraction 📋 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.HasLeftCalculusOfFractions] {X Y : C} (f : L.obj X ⟶ L.obj Y) : ∃ φ, f = φ.map L ⋯ - CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk_eq 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
{C : Type u_1} [CategoryTheory.Category.{u_3, u_1} C] {W : CategoryTheory.MorphismProperty C} [W.HasLeftCalculusOfFractions] {X Y : C} (f : W.LeftFraction X Y) : CategoryTheory.MorphismProperty.LeftFraction.Localization.homMk f = f.map (CategoryTheory.MorphismProperty.LeftFraction.Localization.Q W) ⋯ - 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.LeftFraction.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.LeftFraction.ofInv s hs).map L hL) = CategoryTheory.CategoryStruct.id (L.obj Y) - CategoryTheory.MorphismProperty.LeftFraction.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.LeftFraction.ofInv s hs).map L hL) (L.map s) = CategoryTheory.CategoryStruct.id (L.obj X) - CategoryTheory.MorphismProperty.LeftFraction.map_eq_of_map_eq 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
{C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_4, u_1} C] [CategoryTheory.Category.{u_6, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ₁ φ₂ : W.LeftFraction X Y) {E : Type u_3} [CategoryTheory.Category.{u_5, u_3} E] (L₁ : CategoryTheory.Functor C D) (L₂ : CategoryTheory.Functor C E) [L₁.IsLocalization W] [L₂.IsLocalization W] (h : φ₁.map L₁ ⋯ = φ₂.map L₁ ⋯) : φ₁.map L₂ ⋯ = φ₂.map L₂ ⋯ - CategoryTheory.MorphismProperty.LeftFraction.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.LeftFraction.ofInv s hs).map L hL) h) = h - CategoryTheory.MorphismProperty.LeftFraction.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.LeftFraction.ofInv s hs).map L hL) (CategoryTheory.CategoryStruct.comp (L.map s) h) = h - CategoryTheory.MorphismProperty.LeftFraction.Localization.map_eq_iff 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
{C : Type u_1} [CategoryTheory.Category.{u_3, u_1} C] {W : CategoryTheory.MorphismProperty C} [W.HasLeftCalculusOfFractions] {X Y : C} (f g : W.LeftFraction X Y) : f.map (CategoryTheory.MorphismProperty.LeftFraction.Localization.Q W) ⋯ = g.map (CategoryTheory.MorphismProperty.LeftFraction.Localization.Q W) ⋯ ↔ CategoryTheory.MorphismProperty.LeftFractionRel f g - CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s 📋 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) : CategoryTheory.CategoryStruct.comp (φ.map L hL) (L.map φ.s) = L.map φ.f - CategoryTheory.MorphismProperty.LeftFraction.map_eq 📋 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) [L.IsLocalization W] : φ.map L ⋯ = CategoryTheory.CategoryStruct.comp (L.map φ.f) (CategoryTheory.Localization.isoOfHom L W φ.s ⋯).inv - CategoryTheory.MorphismProperty.LeftFraction.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.LeftFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) : φ.map L hL = CategoryTheory.CategoryStruct.comp (L.map φ.f) (CategoryTheory.inv (L.map φ.s)) - CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_s_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.LeftFraction X Y) (L : CategoryTheory.Functor C D) (hL : W.IsInvertedBy L) {Z : D} (h : L.obj φ.Y' ⟶ Z) : CategoryTheory.CategoryStruct.comp (φ.map L hL) (CategoryTheory.CategoryStruct.comp (L.map φ.s) h) = CategoryTheory.CategoryStruct.comp (L.map φ.f) h - CategoryTheory.MorphismProperty.LeftFraction.map_comp_map_eq_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} [W.HasLeftCalculusOfFractions] {X Y Z : C} (z₁ : W.LeftFraction X Y) (z₂ : W.LeftFraction Y Z) (z₃ : W.LeftFraction z₁.Y' z₂.Y') (h₃ : CategoryTheory.CategoryStruct.comp z₂.f z₃.s = CategoryTheory.CategoryStruct.comp z₁.s z₃.f) (L : CategoryTheory.Functor C D) [L.IsLocalization W] : CategoryTheory.CategoryStruct.comp (z₁.map L ⋯) (z₂.map L ⋯) = (z₁.comp₀ z₂ z₃).map L ⋯ - CategoryTheory.MorphismProperty.LeftFraction.map_compatibility 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions
{C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_4, u_1} C] [CategoryTheory.Category.{u_6, u_2} D] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.LeftFraction X Y) {E : Type u_3} [CategoryTheory.Category.{u_5, u_3} E] (L₁ : CategoryTheory.Functor C D) (L₂ : CategoryTheory.Functor C E) [L₁.IsLocalization W] [L₂.IsLocalization W] : (CategoryTheory.Localization.uniq L₁ L₂ W).functor.map (φ.map L₁ ⋯) = CategoryTheory.CategoryStruct.comp ((CategoryTheory.Localization.compUniqFunctor L₁ L₂ W).hom.app X) (CategoryTheory.CategoryStruct.comp (φ.map L₂ ⋯) ((CategoryTheory.Localization.compUniqFunctor L₁ L₂ W).inv.app Y)) - CategoryTheory.MorphismProperty.LeftFraction₂.map_eq_iff 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions
{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.HasLeftCalculusOfFractions] {X Y : C} (φ ψ : W.LeftFraction₂ X Y) : φ.fst.map L ⋯ = ψ.fst.map L ⋯ ∧ φ.snd.map L ⋯ = ψ.snd.map L ⋯ ↔ CategoryTheory.MorphismProperty.LeftFraction₂Rel φ ψ - CategoryTheory.Localization.exists_leftFraction₂ 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions
{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.HasLeftCalculusOfFractions] {X Y : C} (f f' : L.obj X ⟶ L.obj Y) : ∃ φ, f = φ.fst.map L ⋯ ∧ f' = φ.snd.map L ⋯ - CategoryTheory.Localization.exists_leftFraction₃ 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions
{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.HasLeftCalculusOfFractions] {X Y : C} (f f' f'' : L.obj X ⟶ L.obj Y) : ∃ φ, f = φ.fst.map L ⋯ ∧ f' = φ.snd.map L ⋯ ∧ f'' = φ.thd.map L ⋯ - CategoryTheory.Localization.Preadditive.neg'_eq 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive
{C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_4, u_1} C] [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive C] {L : CategoryTheory.Functor C D} (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasLeftCalculusOfFractions] {X Y : C} (f : L.obj X ⟶ L.obj Y) (φ : W.LeftFraction X Y) (hφ : f = φ.map L ⋯) : CategoryTheory.Localization.Preadditive.neg' W f = φ.neg.map L ⋯ - CategoryTheory.Localization.Preadditive.add'_eq 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive
{C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_4, u_1} C] [CategoryTheory.Category.{u_3, u_2} D] [CategoryTheory.Preadditive C] {L : CategoryTheory.Functor C D} (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.HasLeftCalculusOfFractions] {X Y : C} (f₁ f₂ : L.obj X ⟶ L.obj Y) (φ : W.LeftFraction₂ X Y) (hφ₁ : f₁ = φ.fst.map L ⋯) (hφ₂ : f₂ = φ.snd.map L ⋯) : CategoryTheory.Localization.Preadditive.add' W f₁ f₂ = φ.add.map L ⋯ - CategoryTheory.MorphismProperty.LeftFraction₂.map_add 📋 Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive
{C : Type u_1} {D : Type u_2} [CategoryTheory.Category.{u_3, u_1} C] [CategoryTheory.Category.{u_4, u_2} D] [CategoryTheory.Preadditive C] {W : CategoryTheory.MorphismProperty C} {X Y : C} (φ : W.LeftFraction₂ X Y) (F : CategoryTheory.Functor C D) (hF : W.IsInvertedBy F) [CategoryTheory.Preadditive D] [F.Additive] : φ.add.map F hF = φ.fst.map F hF + φ.snd.map F hF
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 ?aIf 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 ?bBy 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 findtsum_lt_tsumeven though the hypothesisf i < g iis 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