# Is push-forward of coherent sheaves a tensor functor?

Given a finite map between two Noetherian schemes $f: X \rightarrow Y$, is $f_*: \operatorname{Coh}{(X)} \rightarrow \operatorname{Coh}{(Y)}$ a tensor functor? If this is not true in general, is it true if we impose some restriction on the map $f$?

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Maybe this is generally known by others, but what specifically is a tensor functor? –  Jon Beardsley Nov 10 '11 at 19:57
@JBeardz: see here –  t.b. Nov 10 '11 at 20:06
Okay thanks. Is this ever called a "tensored" functor? –  Jon Beardsley Nov 10 '11 at 21:06