A Serre functor on a 
-linear
triangulated category with finite-dimensional morphism spaces
is a 
-linear
autoequivalence 
with bifunctorial duality isomorphisms
 |
Here 
is a field, and the star denotes the dual
vector space over 
.
When it exists, the functor together with its duality
data is unique up to unique natural isomorphism
and commutes with the triangulated shift (Stacks Project n.d.). Serre functors supply
the categorical duality used in Calabi-Yau conditions on derived
categories.
