Lemma 15.64.16. Let R be a ring. Let K, L be objects of D(R).
If K is n-pseudo-coherent and H^ i(K) = 0 for i > a and L is m-pseudo-coherent and H^ j(L) = 0 for j > b, then K \otimes _ R^\mathbf {L} L is t-pseudo-coherent with t = \max (m + a, n + b).
If K and L are pseudo-coherent, then K \otimes _ R^\mathbf {L} L is pseudo-coherent.
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