Loogle!

Result

Found 10 declarations mentioning CategoryTheory.MorphismProperty.Over.map.

• CategoryTheory.MorphismProperty.Over.map 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [P.IsStableUnderComposition] (hPf : P f) : CategoryTheory.Functor (P.Over Q X) (P.Over Q Y)
• CategoryTheory.MorphismProperty.Over.mapPullbackAdj 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] (P Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} (f : X ⟶ Y) [P.IsStableUnderComposition] [P.IsStableUnderBaseChange] [Q.IsStableUnderBaseChange] [CategoryTheory.Limits.HasPullbacks T] [Q.HasOfPostcompProperty Q] (hPf : P f) (hQf : Q f) : CategoryTheory.MorphismProperty.Over.map Q hPf ⊣ CategoryTheory.MorphismProperty.Over.pullback P Q f
• CategoryTheory.MorphismProperty.Over.map.eq_1 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [P.IsStableUnderComposition] (hPf : P f) : CategoryTheory.MorphismProperty.Over.map Q hPf = CategoryTheory.MorphismProperty.Comma.mapRight (CategoryTheory.Functor.id T) (CategoryTheory.Discrete.natTrans fun x => f) ⋯
• CategoryTheory.MorphismProperty.Over.map_comp 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] [P.IsStableUnderComposition] {X Y Z : T} {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) : CategoryTheory.MorphismProperty.Over.map Q ⋯ = (CategoryTheory.MorphismProperty.Over.map Q hf).comp (CategoryTheory.MorphismProperty.Over.map Q hg)
• CategoryTheory.MorphismProperty.Over.map_obj_left 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [P.IsStableUnderComposition] (hPf : P f) (X✝ : CategoryTheory.MorphismProperty.Comma (CategoryTheory.Functor.id T) (CategoryTheory.Functor.fromPUnit X) P Q ⊤) : ((CategoryTheory.MorphismProperty.Over.map Q hPf).obj X✝).left = X✝.left
• CategoryTheory.MorphismProperty.Over.mapComp 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] [P.IsStableUnderComposition] {X Y Z : T} {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) [Q.RespectsIso] : CategoryTheory.MorphismProperty.Over.map Q ⋯ ≅ (CategoryTheory.MorphismProperty.Over.map Q hf).comp (CategoryTheory.MorphismProperty.Over.map Q hg)
• CategoryTheory.MorphismProperty.Over.map_obj_hom 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [P.IsStableUnderComposition] (hPf : P f) (X✝ : CategoryTheory.MorphismProperty.Comma (CategoryTheory.Functor.id T) (CategoryTheory.Functor.fromPUnit X) P Q ⊤) : ((CategoryTheory.MorphismProperty.Over.map Q hPf).obj X✝).hom = CategoryTheory.CategoryStruct.comp X✝.hom f
• CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] [P.IsStableUnderComposition] {X Y Z : T} {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) [Q.RespectsIso] (X✝ : P.Over Q X) : ((CategoryTheory.MorphismProperty.Over.mapComp Q hf hg).hom.app X✝).left = CategoryTheory.CategoryStruct.id X✝.left
• CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] [P.IsStableUnderComposition] {X Y Z : T} {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) [Q.RespectsIso] (X✝ : P.Over Q X) : ((CategoryTheory.MorphismProperty.Over.mapComp Q hf hg).inv.app X✝).left = CategoryTheory.CategoryStruct.id X✝.left
• CategoryTheory.MorphismProperty.Over.map_map_left 📋 Mathlib.CategoryTheory.MorphismProperty.OverAdjunction
  {T : Type u_1} [CategoryTheory.Category.{u_2, u_1} T] {P : CategoryTheory.MorphismProperty T} (Q : CategoryTheory.MorphismProperty T) [Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [P.IsStableUnderComposition] (hPf : P f) {X✝ Y✝ : CategoryTheory.MorphismProperty.Comma (CategoryTheory.Functor.id T) (CategoryTheory.Functor.fromPUnit X) P Q ⊤} (f✝ : X✝ ⟶ Y✝) : ((CategoryTheory.MorphismProperty.Over.map Q hPf).map f✝).left = (CategoryTheory.MorphismProperty.Comma.Hom.hom f✝).left

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