Loogle!

Result

Found 4 declarations mentioning CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map.

• CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map 📋 Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : Type w} [LinearOrder J] [OrderBot J] {F : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone F} {X Y : C} {p : X ⟶ Y} {f : F.obj ⊥ ⟶ X} {g : c.pt ⟶ Y} {j : J} (sq' : CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct c p f g j) {j' : J} (α : j' ⟶ j) : CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct c p f g j'
• CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f' 📋 Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : Type w} [LinearOrder J] [OrderBot J] {F : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone F} {X Y : C} {p : X ⟶ Y} {f : F.obj ⊥ ⟶ X} {g : c.pt ⟶ Y} {j : J} (sq' : CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct c p f g j) {j' : J} (α : j' ⟶ j) : (sq'.map α).f' = CategoryTheory.CategoryStruct.comp (F.map α) sq'.f'
• CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map 📋 Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : Type w} [LinearOrder J] [OrderBot J] {F : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cocone F) {X Y : C} (p : X ⟶ Y) (f : F.obj ⊥ ⟶ X) (g : c.pt ⟶ Y) {X✝ Y✝ : Jᵒᵖ} (α : X✝ ⟶ Y✝) : (CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor c p f g).map α = TypeCat.ofHom fun sq' => sq'.map α.unop
• CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.map_lift 📋 Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting
  {C : Type u} [CategoryTheory.Category.{v, u} C] {J : Type w} [LinearOrder J] [OrderBot J] {F : CategoryTheory.Functor J C} {c : CategoryTheory.Limits.Cocone F} {X Y : C} {p : X ⟶ Y} {f : F.obj ⊥ ⟶ X} {g : c.pt ⟶ Y} [F.IsWellOrderContinuous] {j : J} (hj : Order.IsSuccLimit j) (s : ↑(⋯.functor.op.comp (CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor c p f g)).sections) {i : J} (hij : i < j) : CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map (CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.lift hj s) (CategoryTheory.homOfLE ⋯) = ↑s (Opposite.op ⟨i, hij⟩)

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 88c39f3 serving mathlib revision 9977002