Loogle!

Result

Found 11 declarations mentioning exteriorPower.map.

• exteriorPower.map 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] (n : ℕ) {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : ↥(⋀[R]^n M) →ₗ[R] ↥(⋀[R]^n N)
• exteriorPower.map_id 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} [AddCommGroup M] [Module R M] : exteriorPower.map n LinearMap.id = LinearMap.id
• exteriorPower.map_comp_ιMulti 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : (exteriorPower.map n f).compAlternatingMap (exteriorPower.ιMulti R n) = (exteriorPower.ιMulti R n).compLinearMap f
• exteriorPower.map_comp 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} {N' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] [AddCommGroup N'] [Module R N'] (f : M →ₗ[R] N) (g : N →ₗ[R] N') : exteriorPower.map n (g ∘ₗ f) = exteriorPower.map n g ∘ₗ exteriorPower.map n f
• exteriorPower.zeroEquiv_naturality 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : ↑(exteriorPower.zeroEquiv R N) ∘ₗ exteriorPower.map 0 f = ↑(exteriorPower.zeroEquiv R M)
• exteriorPower.oneEquiv_naturality 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : ↑(exteriorPower.oneEquiv R N) ∘ₗ exteriorPower.map 1 f = f ∘ₗ ↑(exteriorPower.oneEquiv R M)
• exteriorPower.map_apply_ιMulti_family 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] {I : Type u_4} [LinearOrder I] (v : I → M) (f : M →ₗ[R] N) (s : { s // s.card = n }) : (exteriorPower.map n f) (exteriorPower.ιMulti_family R n v s) = exteriorPower.ιMulti_family R n (⇑f ∘ v) s
• exteriorPower.map_comp_ιMulti_family 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] {I : Type u_4} [LinearOrder I] (v : I → M) (f : M →ₗ[R] N) : ⇑(exteriorPower.map n f) ∘ exteriorPower.ιMulti_family R n v = exteriorPower.ιMulti_family R n (⇑f ∘ v)
• exteriorPower.map_apply_ιMulti 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) (m : Fin n → M) : (exteriorPower.map n f) ((exteriorPower.ιMulti R n) m) = (exteriorPower.ιMulti R n) (⇑f ∘ m)
• exteriorPower.map.eq_1 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] (n : ℕ) {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : exteriorPower.map n f = exteriorPower.alternatingMapLinearEquiv ((exteriorPower.ιMulti R n).compLinearMap f)
• exteriorPower.alternatingMapLinearEquiv_symm_map 📋 Mathlib.LinearAlgebra.ExteriorPower.Basic
  {R : Type u} [CommRing R] {n : ℕ} {M : Type u_1} {N : Type u_2} [AddCommGroup M] [Module R M] [AddCommGroup N] [Module R N] (f : M →ₗ[R] N) : exteriorPower.alternatingMapLinearEquiv.symm (exteriorPower.map n f) = (exteriorPower.ιMulti R n).compLinearMap 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 40fea08