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Theorems · Definition · commutative algebra

RingHom.pullbackFst

{R : Type u_1} →
  {S : Type u_2} →
    {T : Type u_3} →
      [inst : Ring R] →
        [inst_1 : Ring S] → [inst_2 : Semiring T] → (f : R →+* T) → (g : S →+* T) → ↥(f.pullback g) →+* R

The first projection from the pullback of f : R →+* T and g : S →+* T to R.

Defined in
Mathlib.RingTheory.LocalRing.Pullback
Cited by
4 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
RingRingSemiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

RingHom.isLocalRing_pullback · cited by 1RingHom.isLocalRing_pullb…RingHom.surjective_pullbackFst_of_surjective · cited by 1RingHom.surjective_pullba…RingHom.pullback_comm_sq · cited by 0RingHom.pullback_comm_sqRingHom.map_pullbackSnd_ker_pullbackFst_eq · cited by 0RingHom.map_pullbackSnd_k…Semiring · cited by 13802SemiringRingHom · cited by 10189RingHomRing · cited by 7463RingRingHom.comp · cited by 899RingHom.compSubring · cited by 602SubringRingHom.fst · cited by 36RingHom.fstSubring.subtype · cited by 22Subring.subtypeRingHom.pullback · cited by 6RingHom.pullbackRingHom.pullbackFstCITED BYCITES

Cites8

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Cited by4

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