Loogle!

Result

Found 12 declarations mentioning CategoryTheory.Functor.OfSequence.map.

• CategoryTheory.Functor.OfSequence.map 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} : ((n : ℕ) → X n ⟶ X (n + 1)) → (i j : ℕ) → i ≤ j → (X i ⟶ X j)
• CategoryTheory.Functor.OfSequence.map_id 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} (f : (n : ℕ) → X n ⟶ X (n + 1)) (i : ℕ) : CategoryTheory.Functor.OfSequence.map f i i ⋯ = CategoryTheory.CategoryStruct.id (X i)
• CategoryTheory.Functor.OfSequence.map_le_succ 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} (f : (n : ℕ) → X n ⟶ X (n + 1)) (i : ℕ) : CategoryTheory.Functor.OfSequence.map f i (i + 1) ⋯ = f i
• CategoryTheory.Functor.OfSequence.map_comp 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} (f : (n : ℕ) → X n ⟶ X (n + 1)) (i j k : ℕ) (hij : i ≤ j) (hjk : j ≤ k) : CategoryTheory.Functor.OfSequence.map f i k ⋯ = CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OfSequence.map f i j hij) (CategoryTheory.Functor.OfSequence.map f j k hjk)
• CategoryTheory.Functor.OfSequence.map.eq_2 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) : CategoryTheory.Functor.OfSequence.map x✝¹ 0 1 = fun x => x✝¹ 0
• CategoryTheory.Functor.OfSequence.map.eq_1 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) : CategoryTheory.Functor.OfSequence.map x✝¹ 0 0 = fun x => CategoryTheory.CategoryStruct.id (x✝ 0)
• CategoryTheory.Functor.OfSequence.map.congr_simp 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} (x✝ x✝¹ : (n : ℕ) → X n ⟶ X (n + 1)) : x✝ = x✝¹ → ∀ (i j : ℕ) (a : i ≤ j), CategoryTheory.Functor.OfSequence.map x✝ i j a = CategoryTheory.Functor.OfSequence.map x✝¹ i j a
• CategoryTheory.Functor.OfSequence.map_comp_assoc 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] {X : ℕ → C} (f : (n : ℕ) → X n ⟶ X (n + 1)) (i j k : ℕ) (hij : i ≤ j) (hjk : j ≤ k) {Z : C} (h : X k ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OfSequence.map f i k ⋯) h = CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OfSequence.map f i j hij) (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OfSequence.map f j k hjk) h)
• CategoryTheory.Functor.OfSequence.map.eq_5 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) (k l : ℕ) : CategoryTheory.Functor.OfSequence.map x✝¹ k.succ l.succ = fun x => CategoryTheory.Functor.OfSequence.map (fun n => x✝¹ (n + 1)) k l ⋯
• CategoryTheory.Functor.OfSequence.map.eq_4 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) (n : ℕ) : CategoryTheory.Functor.OfSequence.map x✝¹ n.succ 0 = fun a => nomatch a
• CategoryTheory.Functor.OfSequence.map.eq_3 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) (l : ℕ) (x_5 : l = 0 → False) : CategoryTheory.Functor.OfSequence.map x✝¹ 0 l.succ = fun x => CategoryTheory.CategoryStruct.comp (x✝¹ 0) (CategoryTheory.Functor.OfSequence.map (fun n => x✝¹ (n + 1)) 0 l ⋯)
• CategoryTheory.Functor.OfSequence.map.eq_def 📋 Mathlib.CategoryTheory.Functor.OfSequence
  {C : Type u_1} [CategoryTheory.Category.{u_2, u_1} C] (x✝ : ℕ → C) (x✝¹ : (n : ℕ) → x✝ n ⟶ x✝ (n + 1)) (x✝² x✝³ : ℕ) : CategoryTheory.Functor.OfSequence.map x✝¹ x✝² x✝³ = match (motive := (x : ℕ → C) → ((n : ℕ) → x n ⟶ x (n + 1)) → (x_2 x_3 : ℕ) → x_2 ≤ x_3 → (x x_2 ⟶ x x_3)) x✝, x✝¹, x✝², x✝³ with | x, x_1, 0, 0 => fun x_2 => CategoryTheory.CategoryStruct.id (x 0) | x, f, 0, 1 => fun x => f 0 | x, f, 0, l.succ => fun x_1 => CategoryTheory.CategoryStruct.comp (f 0) (CategoryTheory.Functor.OfSequence.map (fun n => f (n + 1)) 0 l ⋯) | x, x_1, n.succ, 0 => fun a => nomatch a | x, f, k.succ, l.succ => fun x_1 => CategoryTheory.Functor.OfSequence.map (fun n => f (n + 1)) k l ⋯

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 187ba29 serving mathlib revision 8b227ee