Loogle!

Result

Found 16 declarations mentioning AlgebraicGeometry.AffineSpace.map.

• AlgebraicGeometry.AffineSpace.map 📋 Mathlib.AlgebraicGeometry.AffineSpace
  (n : Type v) {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) : AlgebraicGeometry.AffineSpace n S ⟶ AlgebraicGeometry.AffineSpace n T
• AlgebraicGeometry.AffineSpace.map_id 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} (S : AlgebraicGeometry.Scheme) : AlgebraicGeometry.AffineSpace.map n (CategoryTheory.CategoryStruct.id S) = CategoryTheory.CategoryStruct.id (AlgebraicGeometry.AffineSpace n S)
• AlgebraicGeometry.AffineSpace.map_comp 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S S' S'' : AlgebraicGeometry.Scheme} (f : S ⟶ S') (g : S' ⟶ S'') : AlgebraicGeometry.AffineSpace.map n (CategoryTheory.CategoryStruct.comp f g) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (AlgebraicGeometry.AffineSpace.map n g)
• AlgebraicGeometry.AffineSpace.map_reindex 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n₁ n₂ : Type v} (i : n₁ → n₂) {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n₂ f) (AlgebraicGeometry.AffineSpace.reindex i T) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.reindex i S) (AlgebraicGeometry.AffineSpace.map n₁ f)
• AlgebraicGeometry.AffineSpace.map_toSpecMvPoly 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (AlgebraicGeometry.AffineSpace.toSpecMvPoly n T) = AlgebraicGeometry.AffineSpace.toSpecMvPoly n S
• AlgebraicGeometry.AffineSpace.isPullback_map 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) : CategoryTheory.IsPullback (AlgebraicGeometry.AffineSpace.map n f) (AlgebraicGeometry.AffineSpace n S ↘ S) (AlgebraicGeometry.AffineSpace n T ↘ T) f
• AlgebraicGeometry.AffineSpace.map_over 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (AlgebraicGeometry.AffineSpace n T ↘ T) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace n S ↘ S) f
• AlgebraicGeometry.AffineSpace.functor_obj_map 📋 Mathlib.AlgebraicGeometry.AffineSpace
  (n : Type vᵒᵖ) {X✝ Y✝ : AlgebraicGeometry.Scheme} (f : X✝ ⟶ Y✝) : (AlgebraicGeometry.AffineSpace.functor.obj n).map f = AlgebraicGeometry.AffineSpace.map (Opposite.unop n) f
• AlgebraicGeometry.AffineSpace.map_comp_assoc 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S S' S'' : AlgebraicGeometry.Scheme} (f : S ⟶ S') (g : S' ⟶ S'') {Z : AlgebraicGeometry.Scheme} (h : AlgebraicGeometry.AffineSpace n S'' ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n (CategoryTheory.CategoryStruct.comp f g)) h = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n g) h)
• AlgebraicGeometry.AffineSpace.map_reindex_assoc 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n₁ n₂ : Type v} (i : n₁ → n₂) {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) {Z : AlgebraicGeometry.Scheme} (h : AlgebraicGeometry.AffineSpace n₁ T ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n₂ f) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.reindex i T) h) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.reindex i S) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n₁ f) h)
• AlgebraicGeometry.AffineSpace.map_toSpecMvPoly_assoc 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) {Z : AlgebraicGeometry.Scheme} (h : AlgebraicGeometry.Spec (CommRingCat.of (MvPolynomial n (ULift.{max u v, 0} ℤ))) ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.toSpecMvPoly n T) h) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.toSpecMvPoly n S) h
• AlgebraicGeometry.AffineSpace.map_over_assoc 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) {Z : AlgebraicGeometry.Scheme} (h : T ⟶ Z) : CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.map n f) (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace n T ↘ T) h) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace n S ↘ S) (CategoryTheory.CategoryStruct.comp f h)
• AlgebraicGeometry.AffineSpace.mapSpecMap 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {R S : CommRingCat} (φ : R ⟶ S) : CategoryTheory.Arrow.mk (AlgebraicGeometry.AffineSpace.map n (AlgebraicGeometry.Spec.map φ)) ≅ CategoryTheory.Arrow.mk (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (MvPolynomial.map (CommRingCat.Hom.hom φ))))
• AlgebraicGeometry.AffineSpace.functor_map_app 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n m : Type vᵒᵖ} (i : n ⟶ m) (S : AlgebraicGeometry.Scheme) : (AlgebraicGeometry.AffineSpace.functor.map i).app S = AlgebraicGeometry.AffineSpace.reindex i.unop S
• AlgebraicGeometry.AffineSpace.map_Spec_map 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {R S : CommRingCat} (φ : R ⟶ S) : AlgebraicGeometry.AffineSpace.map n (AlgebraicGeometry.Spec.map φ) = CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.AffineSpace.SpecIso n S).hom (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (MvPolynomial.map (CommRingCat.Hom.hom φ)))) (AlgebraicGeometry.AffineSpace.SpecIso n R).inv)
• AlgebraicGeometry.AffineSpace.map_appTop_coord 📋 Mathlib.AlgebraicGeometry.AffineSpace
  {n : Type v} {S T : AlgebraicGeometry.Scheme} (f : S ⟶ T) (i : n) : (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appTop (AlgebraicGeometry.AffineSpace.map n f))) (AlgebraicGeometry.AffineSpace.coord T i) = AlgebraicGeometry.AffineSpace.coord S i

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