  Let S be a scheme. We compute explicitly the group of homomorphisms, the
S-sheaf of homomorphisms, the group of extensions, and the S-sheaf of
extensions involving locally constant S-group schemes, abelian S-schemes, and
S-tori. Using the obtained results, we study the categories of biextensions
involving these geometrical objets. In particular, we prove that if G_i (for
i=1,2,3) is an extension of an abelian S-scheme A_i by an S-torus T_i, the
category of biextensions of (G_1,G_2) by G_3 is equivalent to the category of
biextensions of the underlying abelian S-schemes (A_1,A_2) by the underlying
S-torus T_3.
