Loogle!

Result

Found 8 declarations mentioning CategoryTheory.Limits.ImageMap.map.

• CategoryTheory.Limits.ImageMap.map 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] {sq : f ⟶ g} (self : CategoryTheory.Limits.ImageMap sq) : CategoryTheory.Limits.image f.hom ⟶ CategoryTheory.Limits.image g.hom
• CategoryTheory.Limits.ImageMap.map_uniq 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] {sq : f ⟶ g} (F G : CategoryTheory.Limits.ImageMap sq) : F.map = G.map
• CategoryTheory.Limits.ImageMap.ext 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} {inst✝ : CategoryTheory.Category.{v, u} C} {f g : CategoryTheory.Arrow C} {inst✝¹ : CategoryTheory.Limits.HasImage f.hom} {inst✝² : CategoryTheory.Limits.HasImage g.hom} {sq : f ⟶ g} {x y : CategoryTheory.Limits.ImageMap sq} (map : x.map = y.map) : x = y
• CategoryTheory.Limits.ImageMap.ext_iff 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} {inst✝ : CategoryTheory.Category.{v, u} C} {f g : CategoryTheory.Arrow C} {inst✝¹ : CategoryTheory.Limits.HasImage f.hom} {inst✝² : CategoryTheory.Limits.HasImage g.hom} {sq : f ⟶ g} {x y : CategoryTheory.Limits.ImageMap sq} : x = y ↔ x.map = y.map
• CategoryTheory.Limits.ImageMap.factor_map_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] (sq : f ⟶ g) (m : CategoryTheory.Limits.ImageMap sq) {Z : C} (h : CategoryTheory.Limits.image g.hom ⟶ Z) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage f.hom) (CategoryTheory.CategoryStruct.comp m.map h) = CategoryTheory.CategoryStruct.comp sq.left (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage g.hom) h)
• CategoryTheory.Limits.ImageMap.map_ι_assoc 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] {sq : f ⟶ g} (self : CategoryTheory.Limits.ImageMap sq) {Z : C} (h : g.right ⟶ Z) : CategoryTheory.CategoryStruct.comp self.map (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι g.hom) h) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι f.hom) (CategoryTheory.CategoryStruct.comp sq.right h)
• CategoryTheory.Limits.ImageMap.factor_map 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] (sq : f ⟶ g) (m : CategoryTheory.Limits.ImageMap sq) : CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.factorThruImage f.hom) m.map = CategoryTheory.CategoryStruct.comp sq.left (CategoryTheory.Limits.factorThruImage g.hom)
• CategoryTheory.Limits.ImageMap.map_ι 📋 Mathlib.CategoryTheory.Limits.Shapes.Images
  {C : Type u} [CategoryTheory.Category.{v, u} C] {f g : CategoryTheory.Arrow C} [CategoryTheory.Limits.HasImage f.hom] [CategoryTheory.Limits.HasImage g.hom] {sq : f ⟶ g} (self : CategoryTheory.Limits.ImageMap sq) : CategoryTheory.CategoryStruct.comp self.map (CategoryTheory.Limits.image.ι g.hom) = CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.image.ι f.hom) sq.right

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