All Questions
Tagged with ring-spectra ct.category-theory
5 questions
3
votes
0
answers
145
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What is the group completion of the underlying multiplicative E∞-monoid of the sphere spectrum?
I recently noticed the following categorical/universal way to describe the passage from Z to Q:
We start with the categroy Setsactv∗ of pointed sets and —...
5
votes
0
answers
120
views
Variations on Thomason's equivalence between connective spectra and symmetric monoidal categories
There's a number of results relating monoidal categories to connective spectra (which are themselves equivalent to E∞-spaces):
Symmetric monoidal categories model all connective ...
5
votes
1
answer
590
views
Does Spec functor sends pushouts of rings into pullbacks of sets?
This question was posted here on StackExchange.
Let A be a commutative ring and B,C be two commutative A-algebras.
Consider the pushout square of ring homomorphism
\require{AMScd}
\begin{CD}
...
12
votes
3
answers
2k
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What is the symmetric monoidal structure on the (\infty,1)-category of spectra?
The (\infty, 1) category Sp of spectra as defined by Lurie in Higher Algebra has the structure of a symmetric monoidal category. Although I know the definition of symmetric monoidal category in ...
9
votes
1
answer
727
views
Schwede-Shipley theorem for monoidal categories?
The Schwede-Shipley theorem gives a criterion for a presentable stable \infty-category to be the category of modules over an \mathcal{E}_1-algebra. Is there any similar criterion for a monoidal ...