Loogle!

Result

Found 5 declarations mentioning Coalgebra.TensorProduct.map.

• Coalgebra.TensorProduct.map 📋 Mathlib.RingTheory.Coalgebra.TensorProduct
  {R : Type u_5} {S : Type u_6} {M : Type u_7} {N : Type u_8} {P : Type u_9} {Q : Type u_10} [CommSemiring R] [CommSemiring S] [Algebra R S] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P] [AddCommMonoid Q] [Module R M] [Module R N] [Module R P] [Module R Q] [Module S M] [IsScalarTower R S M] [Coalgebra S M] [Module S N] [IsScalarTower R S N] [Coalgebra S N] [Coalgebra R P] [Coalgebra R Q] (f : M →ₗc[S] N) (g : P →ₗc[R] Q) : TensorProduct R M P →ₗc[S] TensorProduct R N Q
• Coalgebra.TensorProduct.map_tmul 📋 Mathlib.RingTheory.Coalgebra.TensorProduct
  {R : Type u_5} {S : Type u_6} {M : Type u_7} {N : Type u_8} {P : Type u_9} {Q : Type u_10} [CommSemiring R] [CommSemiring S] [Algebra R S] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P] [AddCommMonoid Q] [Module R M] [Module R N] [Module R P] [Module R Q] [Module S M] [IsScalarTower R S M] [Coalgebra S M] [Module S N] [IsScalarTower R S N] [Coalgebra S N] [Coalgebra R P] [Coalgebra R Q] (f : M →ₗc[S] N) (g : P →ₗc[R] Q) (x : M) (y : P) : (Coalgebra.TensorProduct.map f g) (x ⊗ₜ[R] y) = f x ⊗ₜ[R] g y
• Coalgebra.TensorProduct.map_toLinearMap 📋 Mathlib.RingTheory.Coalgebra.TensorProduct
  {R : Type u_5} {S : Type u_6} {M : Type u_7} {N : Type u_8} {P : Type u_9} {Q : Type u_10} [CommSemiring R] [CommSemiring S] [Algebra R S] [AddCommMonoid M] [AddCommMonoid N] [AddCommMonoid P] [AddCommMonoid Q] [Module R M] [Module R N] [Module R P] [Module R Q] [Module S M] [IsScalarTower R S M] [Coalgebra S M] [Module S N] [IsScalarTower R S N] [Coalgebra S N] [Coalgebra R P] [Coalgebra R Q] (f : M →ₗc[S] N) (g : P →ₗc[R] Q) : ↑(Coalgebra.TensorProduct.map f g) = TensorProduct.AlgebraTensorModule.map ↑f ↑g
• CoalgCat.tensorHom_def 📋 Mathlib.Algebra.Category.CoalgCat.Monoidal
  (R : Type u) [CommRing R] {X₁✝ Y₁✝ X₂✝ Y₂✝ : CoalgCat R} (f : X₁✝ ⟶ Y₁✝) (g : X₂✝ ⟶ Y₂✝) : CategoryTheory.MonoidalCategoryStruct.tensorHom f g = CoalgCat.ofHom (Coalgebra.TensorProduct.map f.toCoalgHom' g.toCoalgHom')
• Bialgebra.TensorProduct.map_toCoalgHom 📋 Mathlib.RingTheory.Bialgebra.TensorProduct
  {R : Type u_1} {S : Type u_2} {A : Type u_3} {B : Type u_4} {C : Type u_5} {D : Type u_6} [CommSemiring R] [CommSemiring S] [Semiring A] [Semiring B] [Bialgebra S A] [Bialgebra R B] [Algebra R A] [Algebra R S] [IsScalarTower R S A] [Semiring C] [Semiring D] [Bialgebra S C] [Bialgebra R D] [Algebra R C] [IsScalarTower R S C] (f : A →ₐc[S] C) (g : B →ₐc[R] D) : ↑(Bialgebra.TensorProduct.map f g) = Coalgebra.TensorProduct.map ↑f ↑g

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 ff04530 serving mathlib revision 8623f65