Theorems · Theorem · group theory
Matrix.SpecialLinearGroup.map_apply_coe
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {S : Type u_1}
[inst_3 : CommRing S] (f : R →+* S) (g : Matrix.SpecialLinearGroup n R),
↑((Matrix.SpecialLinearGroup.map f) g) = f.mapMatrix ↑g- Cited by
- 21 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Matrix.detstatement · cited by 665
- Matrix.SpecialLinearGroupstatement and proof · cited by 348
- Matrix.SpecialLinearGroup.mapstatement and proof · cited by 77
- RingHom.mapMatrixstatement · cited by 55
Cited by21
Results whose statement or proof uses this declaration.
- ModularGroup.SL_neg_smulproof · cited by 5
- Subgroup.strictPeriods_eq_zmultiples_one_of_T_memproof · cited by 4
- isCusp_SL2Z_iffproof · cited by 3
- Matrix.SpecialLinearGroup.map_mapGLproof · cited by 3
- EisensteinSeries.D2_mulproof · cited by 2
- CongruenceSubgroup.strictPeriods_Gammaproof · cited by 2
- Matrix.SpecialLinearGroup.map_intCast_injectiveproof · cited by 2
- OnePoint.exists_mem_SL2proof · cited by 2
- CongruenceSubgroup.exists_Gamma_le_conjproof · cited by 1
- ModularGroup.im_lt_im_S_smulproof · cited by 1
- Derivative.normalizedDerivOfComplex_SL_slashproof · cited by 1
- ModularGroup.smul_eq_lcRow0_addproof · cited by 1