Theorems · Definition · category theory
Action.diagonalSuccIsoTensorDiagonal
(G : Type u) →
[inst : Monoid G] →
(n : ℕ) →
Action.diagonal G (n + 1) ≅
CategoryTheory.MonoidalCategoryStruct.tensorObj (Action.leftRegular G) (Action.diagonal G n)The natural isomorphism of G-sets Gⁿ⁺¹ ≅ G × Gⁿ, where G acts by left multiplication on
each factor.
- Defined in
- Mathlib.CategoryTheory.Action.Monoidal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- Monoidstatement and proof · cited by 3,887
- Equiv.symmproof · cited by 3,681
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- Actionstatement · cited by 206
- Equiv.toIsoproof · cited by 58
- Fin.consEquivproof · cited by 18
- Action.mkIsoproof · cited by 14
- Action.leftRegularstatement · cited by 8
- Action.diagonalstatement · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Action.diagonalSuccIsoTensorDiagonal_hom_homstatement and proof · cited by 1
- Action.diagonalSuccIsoTensorTrivial_inv_hom_applyproof · cited by 1
- Action.diagonalSuccIsoTensorDiagonal_inv_homstatement and proof · cited by 0
- Action.diagonalSuccIsoTensorTrivial_hom_hom_applyproof · cited by 0
- Action.diagonalSuccIsoTensorTrivial.eq_defstatement and proof · cited by 0