Loogle!

Result

Found 12 declarations mentioning AlgebraicGeometry.tilde.map.

• AlgebraicGeometry.tilde.map 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f : M ⟶ N) : AlgebraicGeometry.tilde M ⟶ AlgebraicGeometry.tilde N
• AlgebraicGeometry.tilde.map_id 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M : ModuleCat ↑R} : AlgebraicGeometry.tilde.map (CategoryTheory.CategoryStruct.id M) = CategoryTheory.CategoryStruct.id (AlgebraicGeometry.tilde M)
• AlgebraicGeometry.tilde.map_id_assoc 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M : ModuleCat ↑R} {Z : (AlgebraicGeometry.Spec R).Modules} (h : AlgebraicGeometry.tilde M ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.map (CategoryTheory.CategoryStruct.id M)) h = h
• AlgebraicGeometry.tilde.functor_map 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  (R : CommRingCat) {X✝ Y✝ : ModuleCat ↑R} (f : X✝ ⟶ Y✝) : (AlgebraicGeometry.tilde.functor R).map f = AlgebraicGeometry.tilde.map f
• AlgebraicGeometry.tilde.map_comp 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N P : ModuleCat ↑R} (f : M ⟶ N) (g : N ⟶ P) : AlgebraicGeometry.tilde.map (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.map f) (AlgebraicGeometry.tilde.map g)
• AlgebraicGeometry.tilde.map_zero 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} : AlgebraicGeometry.tilde.map 0 = 0
• AlgebraicGeometry.tilde.map_comp_assoc 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N P : ModuleCat ↑R} (f : M ⟶ N) (g : N ⟶ P) {Z : (AlgebraicGeometry.Spec R).Modules} (h : AlgebraicGeometry.tilde P ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.map (CategoryTheory.CategoryStruct.comp f g)) h = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.map f) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.map g) h)
• AlgebraicGeometry.tilde.map_neg 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f : M ⟶ N) : AlgebraicGeometry.tilde.map (-f) = -AlgebraicGeometry.tilde.map f
• AlgebraicGeometry.tilde.map_sub 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f g : M ⟶ N) : AlgebraicGeometry.tilde.map (f - g) = AlgebraicGeometry.tilde.map f - AlgebraicGeometry.tilde.map g
• AlgebraicGeometry.tilde.map_add 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f g : M ⟶ N) : AlgebraicGeometry.tilde.map (f + g) = AlgebraicGeometry.tilde.map f + AlgebraicGeometry.tilde.map g
• AlgebraicGeometry.tilde.toOpen_map_app 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f : M ⟶ N) (U : TopologicalSpace.Opens (PrimeSpectrum ↑R)) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen M U) ((AlgebraicGeometry.modulesSpecToSheaf.map (AlgebraicGeometry.tilde.map f)).hom.app (Opposite.op U)) = CategoryTheory.CategoryStruct.comp f (AlgebraicGeometry.tilde.toOpen N U)
• AlgebraicGeometry.tilde.toOpen_map_app_assoc 📋 Mathlib.AlgebraicGeometry.Modules.Tilde
  {R : CommRingCat} {M N : ModuleCat ↑R} (f : M ⟶ N) (U : TopologicalSpace.Opens (PrimeSpectrum ↑R)) {Z : ModuleCat ↑R} (h : (AlgebraicGeometry.modulesSpecToSheaf.obj (AlgebraicGeometry.tilde N)).obj.obj (Opposite.op U) ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen M U) (CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.modulesSpecToSheaf.map (AlgebraicGeometry.tilde.map f)).hom.app (Opposite.op U)) h) = CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.tilde.toOpen N U) 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.

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