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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
Defined in
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
Cited by
21 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqFintypeCommRingCommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ModularGroup.SL_neg_smul · cited by 5ModularGroup.SL_neg_smulSubgroup.strictPeriods_eq_zmultiples_one_of_T_mem · cited by 4Subgroup.strictPeriods_eq…isCusp_SL2Z_iff · cited by 3isCusp_SL2Z_iffMatrix.SpecialLinearGroup.map_mapGL · cited by 3SpecialLinearGroup.map_ma…EisensteinSeries.D2_mul · cited by 2EisensteinSeries.D2_mulCongruenceSubgroup.strictPeriods_Gamma · cited by 2CongruenceSubgroup.strict…Matrix.SpecialLinearGroup.map_intCast_injective · cited by 2SpecialLinearGroup.map_in…OnePoint.exists_mem_SL2 · cited by 2OnePoint.exists_mem_SL2CongruenceSubgroup.exists_Gamma_le_conj · cited by 1CongruenceSubgroup.exists…ModularGroup.im_lt_im_S_smul · cited by 1ModularGroup.im_lt_im_S_s…Derivative.normalizedDerivOfComplex_SL_slash · cited by 1Derivative.normalizedDeri…ModularGroup.smul_eq_lcRow0_add · cited by 1ModularGroup.smul_eq_lcRo…SlashInvariantForm.slash_S_apply · cited by 1SlashInvariantForm.slash_…EisensteinSeries.eisSummand_SL2_apply · cited by 1EisensteinSeries.eisSumma…ModularGroup.tendsto_lcRow0 · cited by 1ModularGroup.tendsto_lcRo…DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMonoidHom · cited by 3629MonoidHomMatrix.det · cited by 665Matrix.detMatrix.SpecialLinearGroup · cited by 348Matrix.SpecialLinearGroupMatrix.SpecialLinearGroup.map · cited by 77SpecialLinearGroup.mapRingHom.mapMatrix · cited by 55RingHom.mapMatrixSpecialLinearGroup.map_apply_…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by21

Results whose statement or proof uses this declaration.