If formula_219 and formula_220 are generating sets for "M" and "N", respectively, then formula_221 will be a generating set for formula_222 Because the tensor functor formula_213 sometimes fails to be left exact, this may not be a minimal generating set, even if the original generating sets are minimal. If "M" is a flat module, the functor formula_213 is exact by the very definition of a flat module. If the tensor products are taken over a field "F", we are in the case of vector spaces as above. Since all "F" modules are flat, the bifunctor formula_225 is exact in both positions, and the two given generating sets are bases, then formula_221 indeed forms a basis for formula_227