Theorems · Definition · order theory
IncidenceAlgebra.mu
(𝕜 : Type u_2) →
{α : Type u_5} →
[inst : AddCommGroup 𝕜] →
[One 𝕜] → [inst_2 : Preorder α] → [LocallyFiniteOrder α] → [DecidableEq α] → IncidenceAlgebra 𝕜 αThe Möbius function which inverts zeta as an element of the incidence algebra.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- IncidenceAlgebrastatement · cited by 51
Cited by16
Results whose statement or proof uses this declaration.
- IncidenceAlgebra.mu_mul_zetastatement and proof · cited by 3
- IncidenceAlgebra.mu_toDualstatement and proof · cited by 3
- IncidenceAlgebra.eulerCharproof · cited by 2
- IncidenceAlgebra.zeta_mul_mustatement · cited by 2
- IncidenceAlgebra.mu_applystatement · cited by 2
- IncidenceAlgebra.moebius_inversion_topstatement and proof · cited by 1
- IncidenceAlgebra.mu_eq_neg_sum_Ico_of_nestatement and proof · cited by 1
- IncidenceAlgebra.mu_selfstatement and proof · cited by 1
- IncidenceAlgebra.sum_Icc_mu_leftstatement · cited by 1
- IncidenceAlgebra.sum_Icc_mu_rightstatement and proof · cited by 1
- IncidenceAlgebra.eulerChar_orderDualproof · cited by 0
- IncidenceAlgebra.eulerChar_prodproof · cited by 0