Theorems · Theorem · category theory
CategoryTheory.finrank_endomorphism_simple_eq_one
- 1000+ list: Schur's lemma
∀ {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 : C)
[CategoryTheory.Simple X] [FiniteDimensional 𝕜 (X ⟶ X)], Module.finrank 𝕜 (X ⟶ X) = 1Schur's lemma for endomorphisms in 𝕜-linear categories.
- Defined in
- Mathlib.CategoryTheory.Preadditive.Schur
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Preadditivestatement and proof · cited by 3,309
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- 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
- CategoryTheory.isIso_iff_nonzeroproof · cited by 3
- CategoryTheory.finrank_endomorphism_eq_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.endomorphism_simple_eq_smul_idproof · cited by 1
- FDRep.simple_iff_end_is_rank_oneproof · cited by 1