  We prove that the classical result asserting that the relative Picard group
of a faithfully flat extension of commutative rings is isomorphic to the first
Amitsur cohomology group stills valid in the realm of symmetric monoidal
categories. To this end, we built some group exact sequences from an adjunction
in a bicategory, which are of independent interest. As a particular byproduct
of the evolving theory, we prove a version of Hilbert's theorem 90 for
cocommutatvie coalgebra coextensions (=surjective homomorphisms).
