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feat: more work on node identities

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jstoobysmith 2024-10-18 16:08:17 +00:00
parent d2d75e4d36
commit 0bbc3f4019
6 changed files with 710 additions and 272 deletions
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17
HepLean/Tensors/OverColor/Lift.lean
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@ -664,6 +664,23 @@ lemma obj_μ_tprod_tmul (F : Discrete C ⥤ Rep k G ) (X Y : OverColor C)
discreteSumEquiv F i (HepLean.PiTensorProduct.elimPureTensor p q i) := by
exact μ_tmul_tprod F p q
lemma μIso_inv_tprod (F : Discrete C ⥤ Rep k G ) (X Y : OverColor C)
(p : (i : (X ⊗ Y).left) → F.obj (Discrete.mk <| (X ⊗ Y).hom i)) :
((lift.obj F).μIso X Y).inv.hom (PiTensorProduct.tprod k p) =
(PiTensorProduct.tprod k (fun i => p (Sum.inl i))) ⊗ₜ[k]
(PiTensorProduct.tprod k (fun i => p (Sum.inr i))) := by
change ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).inv (PiTensorProduct.tprod k p) = _
trans ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).toLinearEquiv.symm (PiTensorProduct.tprod k p)
· congr
erw [← LinearEquiv.eq_symm_apply]
change _ = ((lift.obj F).μ X Y).hom _
erw [obj_μ_tprod_tmul]
congr
funext i
match i with
| Sum.inl i => rfl
| Sum.inr i => rfl
end lift
/-- The natural inclusion of `Discrete C` into `OverColor C`. -/
def incl : Discrete C ⥤ OverColor C := Discrete.functor fun c =>