It has been shown that the exactness of Grothendieck exact sequences of type I, of abelian groups and their homomorphisms is preserved by the free functor
F, the polynomial functors
Pn, the
n-th symmetric product functors
Spn, and the direct limit functor lim
→. A necessary and sufficient condition has also been sought under which the polynomial functors
Qn preserve the exactness of Grothendieck exact sequences of type I.
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