Loogle!

Result

Found 14 declarations mentioning Module.Relations.map.

• Module.Relations.map 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) : (relations.R →₀ A) →ₗ[A] relations.G →₀ A
• Module.Relations.map.eq_1 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) : relations.map = Finsupp.linearCombination A relations.relation
• Module.Relations.map_single 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) (r : relations.R) : (relations.map fun₀ | r => 1) = relations.relation r
• Module.Relations.Solution.π_comp_map 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (solution : relations.Solution M) : solution.π ∘ₗ relations.map = 0
• Module.Relations.toQuotient_map 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) : relations.toQuotient ∘ₗ relations.map = 0
• Module.Relations.Solution.π_comp_map_apply 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (solution : relations.Solution M) (x : relations.R →₀ A) : solution.π (relations.map x) = 0
• Module.Relations.Solution.ofπ' 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (π : (relations.G →₀ A) →ₗ[A] M) (hπ : π ∘ₗ relations.map = 0) : relations.Solution M
• Module.Relations.Solution.IsPresentation.exact 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] {solution : relations.Solution M} (h : solution.IsPresentation) : Function.Exact ⇑relations.map ⇑solution.π
• Module.Relations.Solution.ofπ'.eq_1 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (π : (relations.G →₀ A) →ₗ[A] M) (hπ : π ∘ₗ relations.map = 0) : Module.Relations.Solution.ofπ' π hπ = Module.Relations.Solution.ofπ π ⋯
• Module.Relations.toQuotient_map_apply 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) (x : relations.R →₀ A) : relations.toQuotient (relations.map x) = 0
• Module.Relations.Solution.ofπ'_π 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (π : (relations.G →₀ A) →ₗ[A] M) (hπ : π ∘ₗ relations.map = 0) : (Module.Relations.Solution.ofπ' π hπ).π = π
• Module.Relations.range_map 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] (relations : Module.Relations A) : LinearMap.range relations.map = Submodule.span A (Set.range relations.relation)
• Module.Relations.Solution.ofπ'_var 📋 Mathlib.Algebra.Module.Presentation.Basic
  {A : Type u} [Ring A] {relations : Module.Relations A} {M : Type v} [AddCommGroup M] [Module A M] (π : (relations.G →₀ A) →ₗ[A] M) (hπ : π ∘ₗ relations.map = 0) (g : relations.G) : (Module.Relations.Solution.ofπ' π hπ).var g = π fun₀ | g => 1
• Algebra.Presentation.differentials.comm₁₂ 📋 Mathlib.Algebra.Module.Presentation.Differentials
  {R : Type u} {S : Type v} [CommRing R] [CommRing S] [Algebra R S] (pres : Algebra.Presentation R S) : pres.toExtension.cotangentComplex ∘ₗ Algebra.Presentation.differentials.hom₁ pres = ↑pres.cotangentSpaceBasis.repr.symm ∘ₗ pres.differentialsRelations.map

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