Theorems · Theorem · category theory
CategoryTheory.finrank_hom_simple_simple_eq_zero_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] (𝕜 : Type u_2)
[inst_2 : Field 𝕜] [IsAlgClosed 𝕜] [inst_4 : CategoryTheory.Linear 𝕜 C] [CategoryTheory.Limits.HasKernels C] (X Y : C)
[FiniteDimensional 𝕜 (X ⟶ X)] [FiniteDimensional 𝕜 (X ⟶ Y)] [CategoryTheory.Simple X] [CategoryTheory.Simple Y],
Module.finrank 𝕜 (X ⟶ Y) = 0 ↔ IsEmpty (X ≅ Y)- Defined in
- Mathlib.CategoryTheory.Preadditive.Schur
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Fieldstatement and proof · cited by 7,404
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- IsEmptystatement · cited by 759
- IsAlgClosedstatement and proof · cited by 150
- CategoryTheory.Linearstatement and proof · cited by 131
- CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67
- CategoryTheory.Simplestatement and proof · cited by 39
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.finrank_hom_simple_simpleproof · cited by 1