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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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Is there a "Kunneth isomorphism" for internal hom of chain complexes?

If $X^\bullet$ and $Y^\bullet$ are chain complexes over a field, we know from Kunneth theorem that $$H^*((X\otimes Y)^\bullet)\cong H^*(X^\bullet)\otimes H^*(Y^\bullet) $$ I want to know if there is a …
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