Theorems · Theorem · ring theory
RingHomCompTriple.comp_eq
∀ {R₁ : Type u_1} {R₂ : Type u_2} {R₃ : Type u_3} {inst : Semiring R₁} {inst_1 : Semiring R₂} {inst_2 : Semiring R₃}
{σ₁₂ : R₁ →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : outParam (R₁ →+* R₃)} [self : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃],
σ₂₃.comp σ₁₂ = σ₁₃The morphisms form a commutative triangle
- Defined in
- Mathlib.Algebra.Ring.CompTypeclasses
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- RingHomCompTriple
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- RingHom.compstatement · cited by 899
- RingHomCompTriplestatement and proof · cited by 234
Cited by38
Results whose statement or proof uses this declaration.
- RingHomCompTriple.comp_applyproof · cited by 42
- Ideal.Quotient.factor_eqproof · cited by 5
- RingHom.LocalizationAwayPreserves.respectsIsoproof · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- algebraMap_galRestrict'_applyproof · cited by 3
- Ideal.spanIntNorm_localizationproof · cited by 3
- NumberField.InfinitePlace.IsUnramified.finrank_eq_oneproof · cited by 3
- MvPolynomial.exists_rename_eq_of_vars_subset_rangeproof · cited by 3
- FractionalIdeal.canonicalEquiv_canonicalEquivproof · cited by 3
- AlgebraicGeometry.mono_pushoutSection_of_iSup_eqproof · cited by 2
- Algebra.intNorm_eq_of_isLocalizationproof · cited by 1
- Algebra.intTrace_eq_of_isLocalizationproof · cited by 1