Theorems · Definition · group theory
Monoid.CoprodI
{ι : Type u_1} → (M : ι → Type u_2) → [(i : ι) → Monoid (M i)] → Type (max u_1 u_2)The free product (categorical coproduct) of an indexed family of monoids.
- Defined in
- Mathlib.GroupTheory.CoprodI
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Con.Quotientproof · cited by 48
- conGenproof · cited by 23
- Monoid.CoprodI.Relproof · cited by 3
Cited by61
Results whose statement or proof uses this declaration.
- Monoid.CoprodI.ofstatement · cited by 45
- Monoid.CoprodI.liftstatement and proof · cited by 21
- Monoid.CoprodI.Word.prodstatement · cited by 11
- Monoid.CoprodI.NeWord.prodstatement · cited by 9
- Monoid.CoprodI.lift_ofstatement · cited by 8
- Monoid.PushoutI.ofCoprodIstatement · cited by 8
- Monoid.CoprodI.NeWord.append_prodstatement · cited by 4
- Monoid.PushoutI.ofCoprodI_ofstatement · cited by 4
- Monoid.CoprodI.NeWord.prod_singletonstatement · cited by 4
- Monoid.CoprodI.Word.of_smul_defstatement · cited by 4
- Monoid.CoprodI.induction_onstatement and proof · cited by 3
- Monoid.CoprodI.Word.rcons_eq_smulstatement · cited by 3