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Theorems · Definition · group theory

Submonoid.centerCongr

{M : Type u_2} →
  {N : Type u_1} →
    [inst : MulOneClass M] → [inst_1 : MulOneClass N] → M ≃* N → ↥(Submonoid.center M) ≃* ↥(Submonoid.center N)

The center of isomorphic monoids are isomorphic.

Defined in
Mathlib.GroupTheory.Submonoid.Center
Cited by
2 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.centerCongr · cited by 3Subgroup.centerCongrSubmonoid.centerCongr_symm_apply_coe · cited by 0Submonoid.centerCongr_sym…Submonoid.centerCongr_apply_coe · cited by 0Submonoid.centerCongr_app…Submonoid · cited by 3086SubmonoidMulEquiv · cited by 1142MulEquivMulOneClass · cited by 1018MulOneClassSubmonoid.center · cited by 24Submonoid.centerSubsemigroup.centerCongr · cited by 2Subsemigroup.centerCongrSubmonoid.centerCongrCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.