Loogle!

Result

Found 11 declarations mentioning SSet.Subcomplex.Pairing.RankFunction.Cell.map.

• SSet.Subcomplex.Pairing.RankFunction.Cell.map 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : SSet.stdSimplex.obj { len := c.dim + 1 } ⟶ X
• SSet.Subcomplex.Pairing.RankFunction.Cell.preimage_filtration_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] (f : P.RankFunction ι) [P.IsProper] {j : ι} (c : f.Cell j) : (f.filtration j).preimage c.map = c.horn
• SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_image_horn 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : ¬(↑c.s).subcomplex ≤ c.horn.image c.map
• SSet.Subcomplex.Pairing.RankFunction.Cell.range_map 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : SSet.Subcomplex.range c.map = (↑(P.p c.s)).subcomplex
• SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSucc_ι 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} [P.IsProper] {j : ι} [SuccOrder ι] [NoMaxOrder ι] (c : f.Cell j) : CategoryTheory.CategoryStruct.comp c.mapToSucc (f.filtration (Order.succ j)).ι = c.map
• SSet.Subcomplex.Pairing.RankFunction.Cell.image_horn_lt_subcomplex 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : c.horn.image c.map < (↑(P.p c.s)).subcomplex
• SSet.Subcomplex.Pairing.RankFunction.Cell.mapHorn_ι 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] (f : P.RankFunction ι) [P.IsProper] {j : ι} (c : f.Cell j) : CategoryTheory.CategoryStruct.comp (SSet.Subcomplex.Pairing.RankFunction.Cell.mapHorn f c) (f.filtration j).ι = CategoryTheory.CategoryStruct.comp c.horn.ι c.map
• SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSucc_ι_assoc 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} [P.IsProper] {j : ι} [SuccOrder ι] [NoMaxOrder ι] (c : f.Cell j) {Z : SSet} (h : X ⟶ Z) : CategoryTheory.CategoryStruct.comp c.mapToSucc (CategoryTheory.CategoryStruct.comp (f.filtration (Order.succ j)).ι h) = CategoryTheory.CategoryStruct.comp c.map h
• SSet.Subcomplex.Pairing.RankFunction.Cell.image_face_index_compl 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : (SSet.stdSimplex.face {c.index}ᶜ).image c.map = (↑c.s).subcomplex
• SSet.Subcomplex.Pairing.RankFunction.Cell.mapHorn_ι_assoc 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] (f : P.RankFunction ι) [P.IsProper] {j : ι} (c : f.Cell j) {Z : SSet} (h : X ⟶ Z) : CategoryTheory.CategoryStruct.comp (SSet.Subcomplex.Pairing.RankFunction.Cell.mapHorn f c) (CategoryTheory.CategoryStruct.comp (f.filtration j).ι h) = CategoryTheory.CategoryStruct.comp c.horn.ι (CategoryTheory.CategoryStruct.comp c.map h)
• SSet.Subcomplex.Pairing.RankFunction.Cell.map_app_objEquiv_symm_δ_index 📋 Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex
  {X : SSet} {A : X.Subcomplex} {P : A.Pairing} {ι : Type v} [LinearOrder ι] {f : P.RankFunction ι} {i : ι} (c : f.Cell i) [P.IsProper] : (CategoryTheory.ConcreteCategory.hom (c.map.app (Opposite.op { len := c.dim }))) (SSet.stdSimplex.objEquiv.symm (SimplexCategory.δ c.index)) = (↑c.s).simplex

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 88c39f3 serving mathlib revision 9977002