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feat: dualRepIsoDiscrete

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jstoobysmith 2024-11-18 13:58:22 +00:00
parent 5fc5946530
commit ce0805bbdd
11 changed files with 429 additions and 89 deletions
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11
HepLean/Tensors/TensorSpecies/Basic.lean
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@ -556,6 +556,17 @@ lemma tensorToVec_inv_apply_expand (c : S.C) (x : S.FD.obj (Discrete.mk c)) :
rfl)).hom).hom ((OverColor.forgetLiftApp S.FD c).inv.hom x) :=
forgetLiftAppCon_inv_apply_expand S.FD c x
lemma tensorToVec_naturality_eqToHom (c c1 : S.C) (h : c = c1):
(S.tensorToVec c).hom ≫ S.FD.map (Discrete.eqToHom h) =
S.F.map (OverColor.mkIso (by rw [h])).hom ≫ (S.tensorToVec c1).hom :=
OverColor.forgetLiftAppCon_naturality_eqToHom S.FD c c1 h
lemma tensorToVec_naturality_eqToHom_apply (c c1 : S.C) (h : c = c1)
(x : S.F.obj (OverColor.mk ![c])) :
(S.FD.map (Discrete.eqToHom h)).hom ((S.tensorToVec c).hom.hom x) =
(S.tensorToVec c1).hom.hom (((S.F.map (OverColor.mkIso (by rw [h])).hom).hom x)) :=
forgetLiftAppCon_naturality_eqToHom_apply S.FD c c1 h x
end TensorSpecies
end