Theorems · Definition · group theory
SemidirectProduct.inl
{N : Type u_1} → {G : Type u_2} → [inst : Group N] → [inst_1 : Group G] → {φ : G →* MulAut N} → N →* N ⋊[φ] GThe canonical map N →* N ⋊[φ] G sending n to ⟨n, 1⟩
- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, 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 · cited by 69
Cited by21
Results whose statement or proof uses this declaration.
- SemidirectProduct.mk_eq_inl_mul_inrstatement · cited by 3
- SemidirectProduct.toGroupExtensionproof · cited by 3
- SemidirectProduct.left_inlstatement · cited by 1
- SemidirectProduct.lift_inlstatement · cited by 1
- SemidirectProduct.lift_uniquestatement and proof · cited by 1
- SemidirectProduct.map_inlstatement and proof · cited by 1
- SemidirectProduct.range_inl_eq_ker_rightHomstatement and proof · cited by 1
- SemidirectProduct.inl_autstatement and proof · cited by 1
- SemidirectProduct.inl_injectivestatement · cited by 1
- SemidirectProduct.inl_left_mul_inr_rightstatement · cited by 1
- SemidirectProduct.lift_comp_inlstatement · cited by 0
- SemidirectProduct.map_comp_inlstatement · cited by 0