Theorems · Definition · group theory
SemidirectProduct.left
{N : Type u_1} → {G : Type u_2} → [inst : Group N] → [inst_1 : Group G] → {φ : G →* MulAut N} → N ⋊[φ] G → NThe element of N
- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses 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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- MulAutstatement and proof · cited by 158
- SemidirectProductstatement and proof · cited by 69
Cited by35
Results whose statement or proof uses this declaration.
- SemidirectProduct.mapproof · cited by 8
- SemidirectProduct.extstatement and proof · cited by 7
- SemidirectProduct.liftproof · cited by 7
- SemidirectProduct.congrproof · cited by 4
- SemidirectProduct.equivProdproof · cited by 4
- CategoryTheory.ActionCategory.uncurryproof · cited by 2
- SemidirectProduct.inl_autproof · cited by 1
- SemidirectProduct.inl_injectiveproof · cited by 1
- SemidirectProduct.inl_left_mul_inr_rightstatement and proof · cited by 1
- SemidirectProduct.left_inlstatement · cited by 1
- SemidirectProduct.lift_uniqueproof · cited by 1
- SemidirectProduct.map_inlproof · cited by 1