Loogle!

Result

Found 10 declarations mentioning CategoryTheory.Functor.IsStronglyCartesian.map.

• CategoryTheory.Functor.IsStronglyCartesian.map 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' : 𝒮} {a' : 𝒳} {g : R' ⟶ R} {f' : R' ⟶ S} (hf' : f' = CategoryTheory.CategoryStruct.comp g f) (φ' : a' ⟶ b) [p.IsHomLift f' φ'] : a' ⟶ a
• CategoryTheory.Functor.IsStronglyCartesian.map_self 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] : CategoryTheory.Functor.IsStronglyCartesian.map p f φ ⋯ φ = CategoryTheory.CategoryStruct.id a
• CategoryTheory.Functor.IsStronglyCartesian.map_isHomLift 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' : 𝒮} {a' : 𝒳} {g : R' ⟶ R} {f' : R' ⟶ S} (hf' : f' = CategoryTheory.CategoryStruct.comp g f) (φ' : a' ⟶ b) [p.IsHomLift f' φ'] : p.IsHomLift g (CategoryTheory.Functor.IsStronglyCartesian.map p f φ hf' φ')
• CategoryTheory.Functor.IsStronglyCartesian.fac 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' : 𝒮} {a' : 𝒳} {g : R' ⟶ R} {f' : R' ⟶ S} (hf' : f' = CategoryTheory.CategoryStruct.comp g f) (φ' : a' ⟶ b) [p.IsHomLift f' φ'] : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.map p f φ hf' φ') φ = φ'
• CategoryTheory.Functor.IsStronglyCartesian.fac_assoc 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' : 𝒮} {a' : 𝒳} {g : R' ⟶ R} {f' : R' ⟶ S} (hf' : f' = CategoryTheory.CategoryStruct.comp g f) (φ' : a' ⟶ b) [p.IsHomLift f' φ'] {Z : 𝒳} (h : b ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.map p f φ hf' φ') (CategoryTheory.CategoryStruct.comp φ h) = CategoryTheory.CategoryStruct.comp φ' h
• CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso_hom 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R R' S : 𝒮} {a a' b : 𝒳} {f : R ⟶ S} {f' : R' ⟶ S} {g : R' ≅ R} (h : f' = CategoryTheory.CategoryStruct.comp g.hom f) (φ : a ⟶ b) (φ' : a' ⟶ b) [p.IsStronglyCartesian f φ] [p.IsStronglyCartesian f' φ'] : (CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso p h φ φ').hom = CategoryTheory.Functor.IsStronglyCartesian.map p f φ h φ'
• CategoryTheory.Functor.IsStronglyCartesian.map_uniq 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' : 𝒮} {a' : 𝒳} {g : R' ⟶ R} {f' : R' ⟶ S} (hf' : f' = CategoryTheory.CategoryStruct.comp g f) (φ' : a' ⟶ b) [p.IsHomLift f' φ'] (ψ : a' ⟶ a) [p.IsHomLift g ψ] (hψ : CategoryTheory.CategoryStruct.comp ψ φ = φ') : ψ = CategoryTheory.Functor.IsStronglyCartesian.map p f φ hf' φ'
• CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso_inv 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {𝒮 : Type u₁} {𝒳 : Type u₂} [CategoryTheory.Category.{v₁, u₁} 𝒮] [CategoryTheory.Category.{v₂, u₂} 𝒳] (p : CategoryTheory.Functor 𝒳 𝒮) {R R' S : 𝒮} {a a' b : 𝒳} {f : R ⟶ S} {f' : R' ⟶ S} {g : R' ≅ R} (h : f' = CategoryTheory.CategoryStruct.comp g.hom f) (φ : a ⟶ b) (φ' : a' ⟶ b) [p.IsStronglyCartesian f φ] [p.IsStronglyCartesian f' φ'] : (CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso p h φ φ').inv = CategoryTheory.Functor.IsStronglyCartesian.map p f' φ' ⋯ φ
• CategoryTheory.Functor.IsStronglyCartesian.map_comp_map 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' R'' : 𝒮} {a' a'' : 𝒳} {f' : R' ⟶ S} {f'' : R'' ⟶ S} {g : R' ⟶ R} {g' : R'' ⟶ R'} (H : f' = CategoryTheory.CategoryStruct.comp g f) (H' : f'' = CategoryTheory.CategoryStruct.comp g' f') (φ' : a' ⟶ b) (φ'' : a'' ⟶ b) [p.IsStronglyCartesian f' φ'] [p.IsHomLift f'' φ''] : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.map p f' φ' H' φ'') (CategoryTheory.Functor.IsStronglyCartesian.map p f φ H φ') = CategoryTheory.Functor.IsStronglyCartesian.map p f φ ⋯ φ''
• CategoryTheory.Functor.IsStronglyCartesian.map_comp_map_assoc 📋 Mathlib.CategoryTheory.FiberedCategory.Cartesian
  {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.IsStronglyCartesian f φ] {R' R'' : 𝒮} {a' a'' : 𝒳} {f' : R' ⟶ S} {f'' : R'' ⟶ S} {g : R' ⟶ R} {g' : R'' ⟶ R'} (H : f' = CategoryTheory.CategoryStruct.comp g f) (H' : f'' = CategoryTheory.CategoryStruct.comp g' f') (φ' : a' ⟶ b) (φ'' : a'' ⟶ b) [p.IsStronglyCartesian f' φ'] [p.IsHomLift f'' φ''] {Z : 𝒳} (h : a ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.map p f' φ' H' φ'') (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.map p f φ H φ') h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.IsStronglyCartesian.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 bce1d65