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Theorems · Theorem · commutative algebra

IsLocalRing.ResidueField.map_comp_residue

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : IsLocalRing R] [inst_2 : CommRing S]
  [inst_3 : IsLocalRing S] (f : R →+* S) [inst_4 : IsLocalHom f],
  (IsLocalRing.ResidueField.map f).comp (IsLocalRing.residue R) = (IsLocalRing.residue S).comp f
Defined in
Mathlib.RingTheory.LocalRing.ResidueField.Basic
Cited by
1 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsLocalRingCommRingIsLocalRingIsLocalHom
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Around this declaration

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

RingHom.EssFiniteType.residueFieldMap · cited by 0EssFiniteType.residueFiel…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomRingHom.comp · cited by 899RingHom.compIsLocalRing · cited by 339IsLocalRingIsLocalRing.ResidueField · cited by 156IsLocalRing.ResidueFieldIsLocalHom · cited by 100IsLocalHomIsLocalRing.residue · cited by 71IsLocalRing.residueIsLocalRing.ResidueField.map · cited by 16ResidueField.mapResidueField.map_comp_residueCITED BYCITES

Cites8

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Cited by1

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