Loogle!

Result

Found 7 declarations mentioning SSet.Path.map.

• SSet.Path.map 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {X Y : SSet} {n : ℕ} (f : X.Path n) (σ : X ⟶ Y) : Y.Path n
• SSet.Path.map_interval 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {X Y : SSet} {n : ℕ} (f : X.Path n) (σ : X ⟶ Y) (j l : ℕ) (h : j + l ≤ n) : (f.map σ).interval j l h = (f.interval j l h).map σ
• SSet.Path.map_arrow 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {X Y : SSet} {n : ℕ} (f : X.Path n) (σ : X ⟶ Y) (i : Fin n) : (f.map σ).arrow i = σ.app (Opposite.op (SimplexCategory.mk 1)) (f.arrow i)
• SSet.Path.map_vertex 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {X Y : SSet} {n : ℕ} (f : X.Path n) (σ : X ⟶ Y) (i : Fin (n + 1)) : (f.map σ).vertex i = σ.app (Opposite.op (SimplexCategory.mk 0)) (f.vertex i)
• SSet.Subcomplex.map_ι_liftPath 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {X : SSet} (A : X.Subcomplex) {n : ℕ} (p : X.Path n) (hp₀ : ∀ (j : Fin (n + 1)), p.vertex j ∈ A.obj (Opposite.op (SimplexCategory.mk 0))) (hp₁ : ∀ (j : Fin n), p.arrow j ∈ A.obj (Opposite.op (SimplexCategory.mk 1))) : (A.liftPath p hp₀ hp₁).map A.ι = p
• SSet.horn.spineId_map_hornInclusion 📋 Mathlib.AlgebraicTopology.SimplicialSet.Path
  {n : ℕ} (i : Fin (n + 3)) (h₀ : 0 < i) (hₙ : i < Fin.last (n + 2)) : (SSet.horn.spineId i h₀ hₙ).map (SSet.horn (n + 2) i).ι = SSet.stdSimplex.spineId (n + 2)
• SSet.StrictSegal.spineToSimplex_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal
  {X Y : SSet} (sx : X.StrictSegal) (sy : Y.StrictSegal) {n : ℕ} (f : X.Path (n + 1)) (σ : X ⟶ Y) : sy.spineToSimplex (f.map σ) = σ.app (Opposite.op (SimplexCategory.mk (n + 1))) (sx.spineToSimplex f)

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