Loogle!

Result

Found 13 declarations mentioning QuotSMulTop.map.

• QuotSMulTop.map 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] : (M →ₗ[R] M') →ₗ[R] QuotSMulTop r M →ₗ[R] QuotSMulTop r M'
• QuotSMulTop.map_id 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) (M : Type u_1) [AddCommGroup M] [Module R M] : (QuotSMulTop.map r) LinearMap.id = LinearMap.id
• QuotSMulTop.map_surjective 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] {f : M →ₗ[R] M'} (hf : Function.Surjective ⇑f) : Function.Surjective ⇑((QuotSMulTop.map r) f)
• QuotSMulTop.map_apply_mk 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') (x : M) : ((QuotSMulTop.map r) f) (Submodule.Quotient.mk x) = Submodule.Quotient.mk (f x)
• QuotSMulTop.map_comp_mkQ 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') : (QuotSMulTop.map r) f ∘ₗ (r • ⊤).mkQ = (r • ⊤).mkQ ∘ₗ f
• QuotSMulTop.equivQuotTensor_naturality 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') : ↑(QuotSMulTop.equivQuotTensor r M') ∘ₗ (QuotSMulTop.map r) f = LinearMap.lTensor (R ⧸ Ideal.span {r}) f ∘ₗ ↑(QuotSMulTop.equivQuotTensor r M)
• QuotSMulTop.equivTensorQuot_naturality 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') : ↑(QuotSMulTop.equivTensorQuot r M') ∘ₗ (QuotSMulTop.map r) f = LinearMap.rTensor (R ⧸ Ideal.span {r}) f ∘ₗ ↑(QuotSMulTop.equivTensorQuot r M)
• QuotSMulTop.equivQuotTensor_naturality_mk 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') (x : M) : (QuotSMulTop.equivQuotTensor r M') (((QuotSMulTop.map r) f) (Submodule.Quotient.mk x)) = (LinearMap.lTensor (R ⧸ Ideal.span {r}) f) ((QuotSMulTop.equivQuotTensor r M) (Submodule.Quotient.mk x))
• QuotSMulTop.equivTensorQuot_naturality_mk 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] (f : M →ₗ[R] M') (x : M) : (QuotSMulTop.equivTensorQuot r M') (((QuotSMulTop.map r) f) (Submodule.Quotient.mk x)) = (LinearMap.rTensor (R ⧸ Ideal.span {r}) f) ((QuotSMulTop.equivTensorQuot r M) (Submodule.Quotient.mk x))
• QuotSMulTop.map_exact 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} {M'' : Type u_4} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] [AddCommGroup M''] [Module R M''] {f : M →ₗ[R] M'} {g : M' →ₗ[R] M''} (hfg : Function.Exact ⇑f ⇑g) (hg : Function.Surjective ⇑g) : Function.Exact ⇑((QuotSMulTop.map r) f) ⇑((QuotSMulTop.map r) g)
• QuotSMulTop.map_comp 📋 Mathlib.RingTheory.QuotSMulTop
  {R : Type u_2} [CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} {M'' : Type u_4} [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] [AddCommGroup M''] [Module R M''] (g : M' →ₗ[R] M'') (f : M →ₗ[R] M') : (QuotSMulTop.map r) (g ∘ₗ f) = (QuotSMulTop.map r) g ∘ₗ (QuotSMulTop.map r) f
• QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last 📋 Mathlib.RingTheory.Regular.IsSMulRegular
  {R : Type u_1} {M : Type u_3} {M' : Type u_4} {M'' : Type u_5} [CommRing R] [AddCommGroup M] [Module R M] [AddCommGroup M'] [Module R M'] [AddCommGroup M''] [Module R M''] {M''' : Type u_6} [AddCommGroup M'''] [Module R M'''] {r : R} {f₁ : M →ₗ[R] M'} {f₂ : M' →ₗ[R] M''} {f₃ : M'' →ₗ[R] M'''} (h₁₂ : Function.Exact ⇑f₁ ⇑f₂) (h₂₃ : Function.Exact ⇑f₂ ⇑f₃) (h : IsSMulRegular M''' r) : Function.Exact ⇑((QuotSMulTop.map r) f₁) ⇑((QuotSMulTop.map r) f₂)
• Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality 📋 Mathlib.RingTheory.Regular.RegularSequence
  {R : Type u_1} {M : Type u_3} {M₂ : Type u_4} [CommRing R] [AddCommGroup M] [AddCommGroup M₂] [Module R M] [Module R M₂] (r : R) (rs : List R) (f : M →ₗ[R] M₂) : ↑(Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner M₂ r rs) ∘ₗ (Ideal.ofList (r :: rs) • ⊤).mapQ (Ideal.ofList (r :: rs) • ⊤) f ⋯ = (Ideal.ofList rs • ⊤).mapQ (Ideal.ofList rs • ⊤) ((QuotSMulTop.map r) f) ⋯ ∘ₗ ↑(Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner M r rs)

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