Theorems · Theorem · linear algebra
LinearMap.graph_eq_ker_coprod
∀ {R : Type u} {M₃ : Type y} {M₄ : Type z} [inst : Semiring R] [inst_1 : AddCommGroup M₃] [inst_2 : AddCommGroup M₄]
[inst_3 : Module R M₃] [inst_4 : Module R M₄] (g : M₃ →ₗ[R] M₄), g.graph = ((-g).coprod LinearMap.id).ker- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 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.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement · cited by 7,192
- add_commproof · cited by 1,535
- LinearMap.kerstatement · cited by 848
- LinearMap.idstatement · cited by 625
- Submodule.extproof · cited by 204
- LinearMap.coprodstatement · cited by 38
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