If you want to know more how functors are used in Я I recommend you to check out Natural transformation as a basis of control article.
Overview
Functor is a mapping between categories.
Depends the way functors map morphisms they could be either covariant or contravariant.
Covariant functors
Covariant functors map morphisms as it is. We use o letter to designate a c[O]variant (positive) position of an argument (ho, yo, yio, yok, yokl).
Contravariant functors
Contravariant functors flip morphisms. We use a letter to designate a contr[A]variant (negative) position of an argument.
You can compare these functor mapping expressions (fo/fa):
fo : from a o `AR_` into (t a) (t o)
fa : from o a `AR_` into (t a) (t o)Yoneda functors
However I recommend you to use a Yoneda version of these operators (yo/ya):
`yo` : t a `AR_` into (from a o) (t o)
`ya` : t a `AR_` into (from o a) (t o)