Loogle!

Result

Found 6 declarations mentioning CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map.

• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F G H : CategoryTheory.Functor C V} (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) {G' H' : CategoryTheory.Functor C V} (f : G ⟶ G') (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G' H') : H ⟶ H'
• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.right_triangle_components 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F H : CategoryTheory.Functor C V} (G : CategoryTheory.Functor C V) [CategoryTheory.MonoidalCategory.DayConvolution F H] (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) {H' : CategoryTheory.Functor C V} (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F (CategoryTheory.MonoidalCategory.DayConvolution.convolution F H) H') : CategoryTheory.CategoryStruct.comp ℌ'.coev_app (ℌ'.map ℌ.ev_app ℌ) = CategoryTheory.CategoryStruct.id H
• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_app 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F H G : CategoryTheory.Functor C V} [CategoryTheory.MonoidalCategory.DayConvolution F G] (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G) H) {G' H' : CategoryTheory.Functor C V} [CategoryTheory.MonoidalCategory.DayConvolution F G'] (η : G ⟶ G') (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G') H') : CategoryTheory.CategoryStruct.comp η ℌ'.coev_app = CategoryTheory.CategoryStruct.comp ℌ.coev_app (ℌ.map (CategoryTheory.MonoidalCategory.DayConvolution.map (CategoryTheory.CategoryStruct.id F) η) ℌ')
• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_naturality_app 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F G H : CategoryTheory.Functor C V} [CategoryTheory.MonoidalCategory.DayConvolution F H] (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) {G' H' : CategoryTheory.Functor C V} (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G' H') [CategoryTheory.MonoidalCategory.DayConvolution F H'] (η : G ⟶ G') : CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.DayConvolution.map (CategoryTheory.CategoryStruct.id F) (ℌ.map η ℌ')) ℌ'.ev_app = CategoryTheory.CategoryStruct.comp ℌ.ev_app η
• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F G H : CategoryTheory.Functor C V} (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) {G' H' : CategoryTheory.Functor C V} (f : G ⟶ G') (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G' H') (c j : C) : CategoryTheory.CategoryStruct.comp ((ℌ.map f ℌ').app c) (ℌ'.π c j) = CategoryTheory.CategoryStruct.comp (ℌ.π c j) ((CategoryTheory.ihom (F.obj j)).map (f.app (CategoryTheory.MonoidalCategoryStruct.tensorObj j c)))
• CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.map_app_comp_π_assoc 📋 Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [CategoryTheory.Category.{v₂, u₂} V] [CategoryTheory.MonoidalCategory C] [CategoryTheory.MonoidalCategory V] [CategoryTheory.MonoidalClosed V] {F G H : CategoryTheory.Functor C V} (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) {G' H' : CategoryTheory.Functor C V} (f : G ⟶ G') (ℌ' : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G' H') (c j : C) {Z : V} (h : (CategoryTheory.ihom (F.obj j)).obj (G'.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj j c)) ⟶ Z) : CategoryTheory.CategoryStruct.comp ((ℌ.map f ℌ').app c) (CategoryTheory.CategoryStruct.comp (ℌ'.π c j) h) = CategoryTheory.CategoryStruct.comp (ℌ.π c j) (CategoryTheory.CategoryStruct.comp ((CategoryTheory.ihom (F.obj j)).map (f.app (CategoryTheory.MonoidalCategoryStruct.tensorObj j c))) 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.

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