Loogle!

Result

Found 197 declarations mentioning RingHomClass. Of these, 12 match your pattern(s).

• RingHomClass.toRingHom 📋 Mathlib.Algebra.Ring.Hom.Defs
  {F : Type u_1} {α : Type u_2} {β : Type u_3} [FunLike F α β] {x✝ : NonAssocSemiring α} {x✝¹ : NonAssocSemiring β} [RingHomClass F α β] (f : F) : α →+* β
• instCoeTCRingHom 📋 Mathlib.Algebra.Ring.Hom.Defs
  {F : Type u_1} {α : Type u_2} {β : Type u_3} [FunLike F α β] {x✝ : NonAssocSemiring α} {x✝¹ : NonAssocSemiring β} [RingHomClass F α β] : CoeTC F (α →+* β)
• OrderRingHomClass.toOrderRingHom 📋 Mathlib.Algebra.Order.Hom.Ring
  {F : Type u_1} {α : Type u_2} {β : Type u_3} [FunLike F α β] [NonAssocSemiring α] [Preorder α] [NonAssocSemiring β] [Preorder β] [OrderHomClass F α β] [RingHomClass F α β] (f : F) : α →+*o β
• instCoeTCOrderRingHomOfOrderHomClassOfRingHomClass 📋 Mathlib.Algebra.Order.Hom.Ring
  {F : Type u_1} {α : Type u_2} {β : Type u_3} [FunLike F α β] [NonAssocSemiring α] [Preorder α] [NonAssocSemiring β] [Preorder β] [OrderHomClass F α β] [RingHomClass F α β] : CoeTC F (α →+*o β)
• RingHom.ker 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Semiring R] [Semiring S] [FunLike F R S] [rcf : RingHomClass F R S] (f : F) : Ideal R
• Ideal.comap 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Semiring R] [Semiring S] [FunLike F R S] (f : F) [RingHomClass F R S] (I : Ideal S) : Ideal R
• Ideal.mapHom 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [CommSemiring R] [CommSemiring S] [FunLike F R S] [rc : RingHomClass F R S] (f : F) : Ideal R →+* Ideal S
• Ideal.orderEmbeddingOfSurjective 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Semiring R] [Semiring S] [FunLike F R S] (f : F) [RingHomClass F R S] (hf : Function.Surjective ⇑f) : Ideal S ↪o Ideal R
• Ideal.relIsoOfBijective 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Semiring R] [Semiring S] [FunLike F R S] (f : F) [RingHomClass F R S] (hf : Function.Bijective ⇑f) : Ideal S ≃o Ideal R
• Ideal.giMapComap 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Semiring R] [Semiring S] [FunLike F R S] (f : F) [RingHomClass F R S] (hf : Function.Surjective ⇑f) : GaloisInsertion (Ideal.map f) (Ideal.comap f)
• Ideal.relIsoOfSurjective 📋 Mathlib.RingTheory.Ideal.Maps
  {R : Type u} {S : Type v} {F : Type u_1} [Ring R] [Ring S] [FunLike F R S] [RingHomClass F R S] (f : F) (hf : Function.Surjective ⇑f) : Ideal S ≃o { p // Ideal.comap f ⊥ ≤ p }
• RatFunc.mapRingHom 📋 Mathlib.FieldTheory.RatFunc.Basic
  {R : Type u_3} {S : Type u_4} {F : Type u_5} [CommRing R] [CommRing S] [FunLike F (Polynomial R) (Polynomial S)] [RingHomClass F (Polynomial R) (Polynomial S)] (φ : F) (hφ : nonZeroDivisors (Polynomial R) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial S))) : RatFunc R →+* RatFunc S

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 519f454