Preadditive structure on algebras over a monad #
C is a preadditive category and
T is an additive monad on
Algebra T is also
preadditive. Dually, if
U is an additive comonad on
Coalgebra U is preadditive as well.
The category of algebras over an additive monad on a preadditive category is preadditive.
The category of coalgebras over an additive comonad on a preadditive category is preadditive.