  We generalize the construction of the category of 1-motives with torsion
${}^tM_1$ (introduced by Barbieri-Viale, Rosenschon and Saito) as well as the
construction of the category of 1-motivic sheaves ${\rm Shv}_1$ (defined by
Barbieri-Viale and Kahn) to perfect fields $k$ (without inverting the
exponential characteristic). For $k$ transcendental over the prime field we
extend a result of Barbieri-Viale and Kahn, showing that ${}^tM$ and ${\rm
Shv}_1$ have equivalent bounded derived categories.
