Loogle!

Result

Found 6 declarations mentioning SSet.OneTruncation₂.map.

• SSet.OneTruncation₂.map 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {S T : SSet.Truncated 2} (f : S ⟶ T) : SSet.OneTruncation₂ S ⥤rq SSet.OneTruncation₂ T
• SSet.oneTruncation₂_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {X✝ Y✝ : SSet.Truncated 2} (f : X✝ ⟶ Y✝) : SSet.oneTruncation₂.map f = SSet.OneTruncation₂.map f
• SSet.OneTruncation₂.map_obj 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {S T : SSet.Truncated 2} (f : S ⟶ T) (x : SSet.OneTruncation₂ S) : (SSet.OneTruncation₂.map f).obj x = f.app (Opposite.op { obj := SimplexCategory.mk 0, property := SSet.OneTruncation₂._proof_1 }) x
• 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
• CategoryTheory.toNerve₂.ext 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {X : SSet.Truncated 2} {C : Type u} [CategoryTheory.Category.{u, u} C] {F G : X ⟶ (SSet.truncation 2).obj (CategoryTheory.nerve C)} (h : SSet.OneTruncation₂.map F = SSet.OneTruncation₂.map G) : F = G
• SSet.OneTruncation₂.nerve_hom_ext 📋 Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat
  {X : SSet.Truncated 2} {C : Type u} [CategoryTheory.Category.{u, u} C] {F G : X ⟶ (SSet.truncation 2).obj (CategoryTheory.nerve C)} (h : SSet.OneTruncation₂.map F = SSet.OneTruncation₂.map G) : F = G

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