by Michal Marvan
Proc. Winter School on Geometry and Physics, Srni, Jan. 7–14, 1989; Rend. Circ. Mat. Palermo (Ser. II) 22 (1989) Suppl., 161–170.
The horizontal cohomology theory of partial differential equations was developed by A.M. Vinogradov in 1978. In the present paper the horizontal cohomology theory is interpreted as a special case of the Van Osdol bicohomology theory applied to what we call a "jet comonad". It follows that differential equations have well-defined cohomology groups with coefficients in linear differential equations. It is also shown that Janet complexes of the coefficient equations serve as resolutions for this cohomology.