Theorems · Theorem · commutative algebra

CommRingCat.nontrivial_of_isPushout_of_isField

∀ {A B C D : CommRingCat},
  IsField ↑A →
    ∀ {f : A ⟶ B} {g : A ⟶ C} {inl : B ⟶ D} {inr : C ⟶ D} [Nontrivial ↑B] [Nontrivial ↑C],
      CategoryTheory.IsPushout f g inl inr → Nontrivial ↑D

Defined in: Mathlib.Algebra.Category.Ring.LinearAlgebra
Cited by: 0 results in Mathlib
Foundations: Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Nontrivial Nontrivial

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Quiver.Homstatement and proof · cited by 32,603
Algebraproof · cited by 11,388
Equivproof · cited by 8,337
Fieldproof · cited by 7,404
CategoryTheory.Isoproof · cited by 3,963
TensorProductproof · cited by 2,545
Nontrivialstatement and proof · cited by 2,416
CommRingCatstatement and proof · cited by 2,333
CommRingCat.carrierstatement and proof · cited by 1,096
CommRingCat.Hom.homproof · cited by 432
RingHom.toAlgebraproof · cited by 337
CategoryTheory.IsPushoutstatement and proof · cited by 219

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