All Questions
5
questions
7
votes
1
answer
313
views
Are these two notions of unstable localization suitably equivalent?
It seems to me that although homological localization (i.e. formally inverting $E$-homology equivalences for some $E$) is a reasonable thing to do to a spectrum, it's a pretty brutal thing to do to a ...
3
votes
1
answer
233
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
1
answer
166
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
1
answer
450
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 ...
7
votes
0
answers
158
views
Spectral Sequences of Parametrized Spectra
I apologize if this question is of the form "what are some interesting problems in bla" but I was wondering if anybody have studied the following set-up:
Suppose that I have a parametrized spectra $E$...