Loogle!

Result

Found 3 declarations mentioning CommRingCat.KaehlerDifferential.map.

• CommRingCat.KaehlerDifferential.map 📋 Mathlib.Algebra.Category.ModuleCat.Differentials.Basic
  {A B A' B' : CommRingCat} {f : A ⟶ B} {f' : A' ⟶ B'} {g : A ⟶ A'} {g' : B ⟶ B'} (fac : CategoryTheory.CategoryStruct.comp g f' = CategoryTheory.CategoryStruct.comp f g') : CommRingCat.KaehlerDifferential f ⟶ (ModuleCat.restrictScalars (CommRingCat.Hom.hom g')).obj (CommRingCat.KaehlerDifferential f')
• CommRingCat.KaehlerDifferential.map_d 📋 Mathlib.Algebra.Category.ModuleCat.Differentials.Basic
  {A B A' B' : CommRingCat} {f : A ⟶ B} {f' : A' ⟶ B'} {g : A ⟶ A'} {g' : B ⟶ B'} (fac : CategoryTheory.CategoryStruct.comp g f' = CategoryTheory.CategoryStruct.comp f g') (b : ↑B) : (CategoryTheory.ConcreteCategory.hom (CommRingCat.KaehlerDifferential.map fac)) (CommRingCat.KaehlerDifferential.d b) = CommRingCat.KaehlerDifferential.d ((CategoryTheory.ConcreteCategory.hom g') b)
• PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map 📋 Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf
  {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {S' R : CategoryTheory.Functor Dᵒᵖ CommRingCat} (φ' : S' ⟶ R) {X✝ Y✝ : Dᵒᵖ} (f : X✝ ⟶ Y✝) : (PresheafOfModules.DifferentialsConstruction.relativeDifferentials' φ').map f = CommRingCat.KaehlerDifferential.map ⋯

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 bce1d65