Theorems · Theorem · ring theory
TrivSqZeroExt.map_comp_inrHom
∀ {R' : Type u} {M : Type v} [inst : CommSemiring R'] [inst_1 : AddCommMonoid M] [inst_2 : Module R' M]
[inst_3 : Module R'ᵐᵒᵖ M] [inst_4 : IsCentralScalar R' M] {N : Type u_3} [inst_5 : AddCommMonoid N]
[inst_6 : Module R' N] [inst_7 : Module R'ᵐᵒᵖ N] [inst_8 : IsCentralScalar R' N] (f : M →ₗ[R'] N),
(TrivSqZeroExt.map f).toLinearMap ∘ₗ TrivSqZeroExt.inrHom R' M = TrivSqZeroExt.inrHom R' N ∘ₗ f- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- LinearMap.compstatement · cited by 1,642
- MulOppositestatement and proof · cited by 1,135
- LinearMap.extproof · cited by 844
- AlgHom.toLinearMapstatement · cited by 254
- TrivSqZeroExtstatement · cited by 180
- IsCentralScalarstatement and proof · cited by 39
- TrivSqZeroExt.inrHomstatement · cited by 16
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