Loogle!

Result

Found 9 declarations mentioning SSet.Truncated.Edge.map.

• SSet.Truncated.Edge.map 📋 Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
  {X Y : SSet.Truncated 2} {x₀ x₁ : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 })} (e : SSet.Truncated.Edge x₀ x₁) (f : X ⟶ Y) : SSet.Truncated.Edge (f.app (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 }) x₀) (f.app (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 }) x₁)
• SSet.Truncated.Edge.map_id 📋 Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
  {X Y : SSet.Truncated 2} (x : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 })) (f : X ⟶ Y) : (SSet.Truncated.Edge.id x).map f = SSet.Truncated.Edge.id (f.app (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 }) x)
• SSet.Truncated.Edge.map_edge 📋 Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
  {X Y : SSet.Truncated 2} {x₀ x₁ : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 })} (e : SSet.Truncated.Edge x₀ x₁) (f : X ⟶ Y) : (e.map f).edge = f.app (Opposite.op { obj := SimplexCategory.mk 1, property := SSet.Truncated.Edge._proof_2 }) e.edge
• SSet.Truncated.Edge.CompStruct.map 📋 Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
  {X Y : SSet.Truncated 2} {x₀ x₁ x₂ : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 })} {e₀₁ : SSet.Truncated.Edge x₀ x₁} {e₁₂ : SSet.Truncated.Edge x₁ x₂} {e₀₂ : SSet.Truncated.Edge x₀ x₂} (h : e₀₁.CompStruct e₁₂ e₀₂) (f : X ⟶ Y) : (e₀₁.map f).CompStruct (e₁₂.map f) (e₀₂.map f)
• SSet.Truncated.Edge.CompStruct.map_simplex 📋 Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
  {X Y : SSet.Truncated 2} {x₀ x₁ x₂ : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.Truncated.Edge._proof_1 })} {e₀₁ : SSet.Truncated.Edge x₀ x₁} {e₁₂ : SSet.Truncated.Edge x₁ x₂} {e₀₂ : SSet.Truncated.Edge x₀ x₂} (h : e₀₁.CompStruct e₁₂ e₀₂) (f : X ⟶ Y) : (h.map f).simplex = f.app (Opposite.op { obj := SimplexCategory.mk 2, property := SSet.Truncated.Edge.CompStruct._proof_1 }) h.simplex
• SSet.OneTruncation₂.map_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {S T : SSet.Truncated 2} (f : S ⟶ T) {X✝ Y✝ : SSet.OneTruncation₂ S} (e : X✝ ⟶ Y✝) : (SSet.OneTruncation₂.map f).map e = SSet.Truncated.Edge.map e f
• SSet.Truncated.mapHomotopyCategory_homMk 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {V W : SSet.Truncated 2} (f : V ⟶ W) {x y : V.obj (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.OneTruncation₂._proof_1 })} (e : SSet.Truncated.Edge x y) : (SSet.Truncated.mapHomotopyCategory f).map (SSet.Truncated.HomotopyCategory.homMk e) = SSet.Truncated.HomotopyCategory.homMk (e.map f)
• SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk 📋 Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction
  {X : SSet.Truncated 2} {C : Type u} [CategoryTheory.SmallCategory C] (φ : X ⟶ (SSet.truncation 2).obj (CategoryTheory.nerve C)) {x₀ x₁ : X.obj (Opposite.op { obj := SimplexCategory.mk 0, property := _proof_11✝ })} (e : SSet.Truncated.Edge x₀ x₁) : (SSet.Truncated.HomotopyCategory.descOfTruncation φ).map (SSet.Truncated.HomotopyCategory.homMk e) = CategoryTheory.nerve.homEquiv (e.map φ)
• CategoryTheory.nerve.functorOfNerveMap_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction
  {C D : Type u} [CategoryTheory.SmallCategory C] [CategoryTheory.SmallCategory D] (φ : CategoryTheory.Nerve.nerveFunctor₂.obj (CategoryTheory.Cat.of C) ⟶ CategoryTheory.Nerve.nerveFunctor₂.obj (CategoryTheory.Cat.of D)) {X✝ Y✝ : C} (f : X✝ ⟶ Y✝) : (CategoryTheory.nerve.functorOfNerveMap φ).map f = CategoryTheory.nerve.homEquiv ((CategoryTheory.nerve.edgeMk f).toTruncated.map φ)

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 6ff4759 serving mathlib revision edaf32c