Duality-intertwining morphisms are invertible #
The per-object kernel of Deligne 3.2: a morphism compatible with exact pairings on both sides is an isomorphism, with inverse the mate of its partner. A monoidal natural transformation between fibre functors supplies exactly this data at every object.
noncomputable def
RS.dualityMate
{D : Type u}
[CategoryTheory.Category.{v, u} D]
[CategoryTheory.MonoidalCategory D]
{X X' Y Y' : D}
[CategoryTheory.ExactPairing X X']
[CategoryTheory.ExactPairing Y Y']
(f' : X' ⟶ Y')
:
The mate of the partner: the candidate inverse.
Equations
- One or more equations did not get rendered due to their size.