Loogle!

Result

Found 8 declarations mentioning CategoryTheory.Functor.IsStronglyCocartesian.map.

• CategoryTheory.Functor.IsStronglyCocartesian.map 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' : 𝒮} {b' : 𝒳} {g : S ⟶ S'} {f' : R ⟶ S'} (hf' : f' = CategoryTheory.CategoryStruct.comp f g) (φ' : a ⟶ b') [p.IsHomLift f' φ'] : b ⟶ b'
• CategoryTheory.Functor.IsStronglyCocartesian.map_self 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] : CategoryTheory.Functor.IsStronglyCocartesian.map p f φ ⋯ φ = CategoryTheory.CategoryStruct.id b
• CategoryTheory.Functor.IsStronglyCocartesian.map_isHomLift 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' : 𝒮} {b' : 𝒳} {g : S ⟶ S'} {f' : R ⟶ S'} (hf' : f' = CategoryTheory.CategoryStruct.comp f g) (φ' : a ⟶ b') [p.IsHomLift f' φ'] : p.IsHomLift g (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ hf' φ')
• CategoryTheory.Functor.IsStronglyCocartesian.fac 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' : 𝒮} {b' : 𝒳} {g : S ⟶ S'} {f' : R ⟶ S'} (hf' : f' = CategoryTheory.CategoryStruct.comp f g) (φ' : a ⟶ b') [p.IsHomLift f' φ'] : CategoryTheory.CategoryStruct.comp φ (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ hf' φ') = φ'
• CategoryTheory.Functor.IsStronglyCocartesian.fac_assoc 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' : 𝒮} {b' : 𝒳} {g : S ⟶ S'} {f' : R ⟶ S'} (hf' : f' = CategoryTheory.CategoryStruct.comp f g) (φ' : a ⟶ b') [p.IsHomLift f' φ'] {Z : 𝒳} (h : b' ⟶ Z) : CategoryTheory.CategoryStruct.comp φ (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ hf' φ') h) = CategoryTheory.CategoryStruct.comp φ' h
• CategoryTheory.Functor.IsStronglyCocartesian.map_uniq 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' : 𝒮} {b' : 𝒳} {g : S ⟶ S'} {f' : R ⟶ S'} (hf' : f' = CategoryTheory.CategoryStruct.comp f g) (φ' : a ⟶ b') [p.IsHomLift f' φ'] (ψ : b ⟶ b') [p.IsHomLift g ψ] (hψ : CategoryTheory.CategoryStruct.comp φ ψ = φ') : ψ = CategoryTheory.Functor.IsStronglyCocartesian.map p f φ hf' φ'
• CategoryTheory.Functor.IsStronglyCocartesian.map_comp_map 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' S'' : 𝒮} {b' b'' : 𝒳} {f' : R ⟶ S'} {f'' : R ⟶ S''} {g : S ⟶ S'} {g' : S' ⟶ S''} (H : f' = CategoryTheory.CategoryStruct.comp f g) (H' : f'' = CategoryTheory.CategoryStruct.comp f' g') (φ' : a ⟶ b') (φ'' : a ⟶ b'') [p.IsStronglyCocartesian f' φ'] [p.IsHomLift f'' φ''] : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ H φ') (CategoryTheory.Functor.IsStronglyCocartesian.map p f' φ' H' φ'') = CategoryTheory.Functor.IsStronglyCocartesian.map p f φ ⋯ φ''
• CategoryTheory.Functor.IsStronglyCocartesian.map_comp_map_assoc 📋 Mathlib.CategoryTheory.FiberedCategory.Cocartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R S : 𝒮} {a b : 𝒳} (f : R ⟶ S) (φ : a ⟶ b) [p.IsStronglyCocartesian f φ] {S' S'' : 𝒮} {b' b'' : 𝒳} {f' : R ⟶ S'} {f'' : R ⟶ S''} {g : S ⟶ S'} {g' : S' ⟶ S''} (H : f' = CategoryTheory.CategoryStruct.comp f g) (H' : f'' = CategoryTheory.CategoryStruct.comp f' g') (φ' : a ⟶ b') (φ'' : a ⟶ b'') [p.IsStronglyCocartesian f' φ'] [p.IsHomLift f'' φ''] {Z : 𝒳} (h : b'' ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ H φ') (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCocartesian.map p f' φ' H' φ'') h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCocartesian.map p f φ ⋯ φ'') 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 19971e9 serving mathlib revision 40fea08