Theorems · Theorem · group theory
Monoid.CoprodI.mrange_eq_iSup
∀ {ι : Type u_1} {M : ι → Type u_2} [inst : (i : ι) → Monoid (M i)] {N : Type u_4} [inst_1 : Monoid N]
(f : (i : ι) → M i →* N), MonoidHom.mrange (Monoid.CoprodI.lift f) = ⨆ i, MonoidHom.mrange (f i)- Defined in
- Mathlib.GroupTheory.CoprodI
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Equivstatement and proof · cited by 8,337
- Set.rangeproof · cited by 4,705
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement and proof · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- iSupstatement and proof · cited by 2,415
- MonoidHom.compproof · cited by 469
- Submonoid.closureproof · cited by 167
- MonoidHom.mrangestatement and proof · cited by 63
- Monoid.CoprodIstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.CoprodI.lift_mrange_leproof · cited by 0