Let $X$ be a CW-spectrum. It is well-known that $[\_ ,X]$ is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about $[X, \_]$? Is it a homology theory? (I do not claim every homology is corepresented by a spectrum).

Let $X$ be a CW-spectrum. It is well-known that $[\_ ,X]$ is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about $[X, \_]$? Is it a homology theory? (I do not claim every homology is corepresented by a spectrum.)

Let $X$ be a CW-spectrum. It is well-known that $[\_ ,X]$ is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about $[X, \_]$? Is it a homology theory? (I do not claim every homology is corepresented by a spectrum.)

Let $X$ be a CW-spectrum. It is well-known that $[\_ ,X]$ is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about $[X, \_]$? Is it a homology theory? (I do not claim every homology is corepresented by a spectrum).

Let $X$ be a CW-spectrum, it is well-known that [ _ ,X] is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about [X, _ ]?, is it a homology theory? (I do not claim every homology is corepresented by a spectrum). Thanks!.

Let $X$ be a CW-spectrum. It is well-known that $[\_ ,X]$ is a generalized cohomology theory and, by Brown's representability theorem, every generalized theory is $H$ represented by a spectrum (namely, $H$ has this form).

What about $[X, \_]$? Is it a homology theory? (I do not claim every homology is corepresented by a spectrum.)