Section SigmaSAFunctor.
Variable I:Type.
Variables (F: I -> functor).
Variables (JOIN: forall i A, Join (F i A))
(fSA : forall i, pafunctor (F i) (JOIN i)).
Existing Instance Join_sigma.
Hypothesis inj_sig : forall A i x y,
existT (fun i => F i A) i x = existT (fun i => F i A) i y -> x = y.

Lemma paf_sigma : @pafunctor (fsig F)
(fun A => Join_sigma I (fun i => F i A) (fun i => JOIN i A)).