Loogle!

Result

Found 4 declarations mentioning CategoryTheory.Limits.PullbackCone.map.

• CategoryTheory.Limits.PullbackCone.map 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} (c : CategoryTheory.Limits.PullbackCone f g) (G : CategoryTheory.Functor C D) : CategoryTheory.Limits.PullbackCone (G.map f) (G.map g)
• CategoryTheory.Limits.PullbackCone.isLimitMapConeEquiv 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z} (c : CategoryTheory.Limits.PullbackCone f g) (G : CategoryTheory.Functor C D) : CategoryTheory.Limits.IsLimit (G.mapCone c) ≃ CategoryTheory.Limits.IsLimit (c.map G)
• CategoryTheory.Limits.PullbackCone.isLimitCoyonedaEquiv 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z) (c : CategoryTheory.Limits.PullbackCone f g) : CategoryTheory.Limits.IsLimit c ≃ ((X_1 : Cᵒᵖ) → CategoryTheory.Limits.IsLimit (c.map (CategoryTheory.coyoneda.obj X_1)))
• CategoryTheory.Limits.PushoutCocone.isColimitYonedaEquiv 📋 Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} {f : X ⟶ Y} {g : X ⟶ Z} (c : CategoryTheory.Limits.PushoutCocone f g) : CategoryTheory.Limits.IsColimit c ≃ ((X_1 : C) → CategoryTheory.Limits.IsLimit (c.op.map (CategoryTheory.yoneda.obj X_1)))

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