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Theorems · Theorem · commutative algebra

RingHom.prodMap_def

∀ {R : Type u_1} {R' : Type u_2} {S : Type u_3} {S' : Type u_4} [inst : NonAssocSemiring R]
  [inst_1 : NonAssocSemiring S] [inst_2 : NonAssocSemiring R'] [inst_3 : NonAssocSemiring S'] (f : R →+* R')
  (g : S →+* S'), f.prodMap g = (f.comp (RingHom.fst R S)).prod (g.comp (RingHom.snd R S))
Defined in
Mathlib.Algebra.Ring.Prod
Cited by
0 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
NonAssocSemiringNonAssocSemiringNonAssocSemiringNonAssocSemiring
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RingHom · cited by 10189RingHomRingHom.comp · cited by 899RingHom.compNonAssocSemiring · cited by 805NonAssocSemiringRingHom.snd · cited by 39RingHom.sndRingHom.fst · cited by 36RingHom.fstRingHom.prod · cited by 8RingHom.prodRingHom.prodMap · cited by 6RingHom.prodMapRingHom.prodMap_defCITED BYCITES

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