## On the horizontal cohomology with general coefficients

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.

Zbl 0712.35005