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3 votes
0 answers
145 views

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 —...
Emily's user avatar
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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 ...
Emily's user avatar
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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} ...
Fabio Lucchini's user avatar
12 votes
3 answers
2k views

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 ...
Exit path's user avatar
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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 ...
abc.xyz's user avatar
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