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David Roberts ♦
David Roberts ♦
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Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$$X^+={\rm Hom}_Z(X, \mathbb{Q}/\mathbb{Z})$. Is it true to say that $X^+$ is a dg-injective chain complex?

Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$. Is it true to say that $X^+$ is a dg-injective chain complex?

Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \mathbb{Q}/\mathbb{Z})$. Is it true to say that $X^+$ is a dg-injective chain complex?

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user38585
user38585
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Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$. Is it true to say that $X^+\otimes E$$X^+$ is a dg-injective chain complex?

Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$. Is it true to say that $X^+\otimes E$ is a dg-injective chain complex?

Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$. Is it true to say that $X^+$ is a dg-injective chain complex?

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user38585
user38585
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dg-flat complexes and their characters

Let $\otimes$ denotes the usual tensor products of complexes and symbols live in the category of chain complexes of $R$-modules. Let $X$ be a dg-flat complex (i.e. $X_n$ is flat for each n and $X\otimes E$ is exact for each exact complex E). We can define a new complex $X^+={\rm Hom}_Z(X, \frac{Q}{Z})$. Is it true to say that $X^+\otimes E$ is a dg-injective chain complex?