DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

feat: Expansion lemmas for units

Browse source
This commit is contained in:
jstoobysmith 2024-10-24 15:04:37 +00:00
parent 28e0e4d610
commit 14377da3d8
4 changed files with 131 additions and 3 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/Tensors/Tree/Basic.lean
View file

@ -64,20 +64,22 @@ structure TensorSpecies where
/-- The unit is symmetric. -/
unit_symm (c : C) :
((unit.app (Discrete.mk c)).hom (1 : k)) =
((FDiscrete.obj (Discrete.mk (τ (c)))) ◁ (FDiscrete.map (Discrete.eqToHom (τ_involution c)))).hom
((FDiscrete.obj (Discrete.mk (τ (c)))) ◁
(FDiscrete.map (Discrete.eqToHom (τ_involution c)))).hom
((β_ (FDiscrete.obj (Discrete.mk (τ (τ c)))) (FDiscrete.obj (Discrete.mk (τ (c))))).hom.hom
((unit.app (Discrete.mk (τ c))).hom (1 : k)))
/-- On contracting metrics we get back the unit. -/
contr_metric (c : C) :
(β_ (FDiscrete.obj (Discrete.mk c)) (FDiscrete.obj (Discrete.mk (τ c)))).hom.hom
(((FDiscrete.obj (Discrete.mk c)) ◁ (λ_ (FDiscrete.obj (Discrete.mk (τ c)))).hom).hom
(((FDiscrete.obj (Discrete.mk c)) ◁ (λ_ (FDiscrete.obj (Discrete.mk (τ c)))).hom).hom
(((FDiscrete.obj (Discrete.mk c)) ◁ ((contr.app (Discrete.mk c)) ▷
(FDiscrete.obj (Discrete.mk (τ c))))).hom
(((FDiscrete.obj (Discrete.mk c)) ◁ (α_ (FDiscrete.obj (Discrete.mk (c)))
(FDiscrete.obj (Discrete.mk (τ c))) (FDiscrete.obj (Discrete.mk (τ c)))).inv).hom
((α_ (FDiscrete.obj (Discrete.mk (c))) (FDiscrete.obj (Discrete.mk (c)))
(FDiscrete.obj (Discrete.mk (τ c)) ⊗ FDiscrete.obj (Discrete.mk (τ c)))).hom.hom
((metric.app (Discrete.mk c)).hom (1 : k) ⊗ₜ[k] (metric.app (Discrete.mk (τ c))).hom (1 : k))))))
((metric.app (Discrete.mk c)).hom (1 : k) ⊗ₜ[k]
(metric.app (Discrete.mk (τ c))).hom (1 : k))))))
= (unit.app (Discrete.mk c)).hom (1 : k)
noncomputable section