Loogle!

Result

Found 5 declarations mentioning CategoryTheory.ShiftedHom.map.

• CategoryTheory.ShiftedHom.map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
  {C : Type u_1} [CategoryTheory.Category.{u_5, u_1} C] {D : Type u_2} [CategoryTheory.Category.{u_6, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] : CategoryTheory.ShiftedHom (F.obj X) (F.obj Y) a
• CategoryTheory.ShiftedHom.id_map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
  {C : Type u_1} [CategoryTheory.Category.{u_5, u_1} C] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) : f.map (CategoryTheory.Functor.id C) = f
• CategoryTheory.ShiftedHom.comp_map 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
  {C : Type u_1} [CategoryTheory.Category.{u_5, u_1} C] {D : Type u_2} [CategoryTheory.Category.{u_6, u_2} D] {E : Type u_3} [CategoryTheory.Category.{u_7, u_3} E] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] [CategoryTheory.HasShift E M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] (G : CategoryTheory.Functor D E) [G.CommShift M] : f.map (F.comp G) = (f.map F).map G
• CategoryTheory.ShiftedHom.map_comp 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
  {C : Type u_1} [CategoryTheory.Category.{u_5, u_1} C] {D : Type u_2} [CategoryTheory.Category.{u_6, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y Z : C} {a b c : M} (f : CategoryTheory.ShiftedHom X Y a) (g : CategoryTheory.ShiftedHom Y Z b) (h : b + a = c) (F : CategoryTheory.Functor C D) [F.CommShift M] : (f.comp g h).map F = (f.map F).comp (g.map F) h
• CategoryTheory.ShiftedHom.map.eq_1 📋 Mathlib.CategoryTheory.Shift.ShiftedHom
  {C : Type u_1} [CategoryTheory.Category.{u_5, u_1} C] {D : Type u_2} [CategoryTheory.Category.{u_6, u_2} D] {M : Type u_4} [AddMonoid M] [CategoryTheory.HasShift C M] [CategoryTheory.HasShift D M] {X Y : C} {a : M} (f : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [F.CommShift M] : f.map F = CategoryTheory.CategoryStruct.comp (F.map f) ((F.commShiftIso a).hom.app Y)

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 40fea08