Theorems · Theorem · ring theory
TrivSqZeroExt.map_inr
∀ {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) (x : M),
(TrivSqZeroExt.map f) (TrivSqZeroExt.inr x) = TrivSqZeroExt.inr (f x)- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- AlgHomstatement and proof · cited by 3,236
- LinearMap.compproof · cited by 1,642
- MulOppositestatement and proof · cited by 1,135
- TrivSqZeroExtstatement and proof · cited by 180
- Algebra.ofIdproof · cited by 166
- LinearMap.comp_applyproof · cited by 76
Cited by4
Results whose statement or proof uses this declaration.
- ExteriorAlgebra.toTrivSqZeroExt_comp_mapproof · cited by 1
- TrivSqZeroExt.map_comp_inrHomproof · cited by 0
- TrivSqZeroExt.map_comp_mapproof · cited by 0
- TrivSqZeroExt.map_idproof · cited by 0