Questions tagged [parameterized-homotopy]

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10
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2answers
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Rational parameterized spectra

Consider the homotopical category of rational dg-modules. I suppose this ought to present the rationalization of the homotopy theory of parameterized spectra. Has such "rational parameterized stable ...
3
votes
1answer
213 views

Morphisms of parametrized ring spectra

This is a follow-up to this question, in which Denis Nardin nicely explained that $$ \operatorname{Map}_{\operatorname{Fun}(X, \operatorname{Sp})}(E_X, E'_X) \simeq \operatorname{Map}(X, \operatorname{...
2
votes
1answer
152 views

Are morphisms of parametrized spectra themselves parametrized morphisms of spectra?

Let $X$ be a fixed parametrizing space. Let $E$ and $E'$ be two spectra and let $E_X$ and $E'_X$ be their trivial parametrized versions. Intuitively I imagine that the morphisms of parametrized ...
8
votes
1answer
340 views

Parametrized Dold-Kan correspondence?

The stable Dold-Kan correspondence says that for every commutative ring $R$, there is an equivalence of $\infty$-categories between the category $Ch(R)$ of (unbounded) chain complexes of $R$-modules ...