Module spectrum
In algebra, a module spectrum is a spectrum with an action of a ring spectrum; it generalizes a module in abstract algebra.
The ∞-category of (say right) module spectra is stable; hence, it can be considered as either analog or generalization of the derived category of modules over a ring.
K-theory
Lurie defines the K-theory of a ring spectrum R to be the K-theory of the ∞-category of perfect modules over R (a perfect module being defined as a compact object in the ∞-category of module spectra.)
gollark: Please, 34k karma is easy to get.
gollark: Protocol χ-38 has already been activated in response. No further action is required.
gollark: Jerdle is Jerdle. No further questions are to be taken at this time on the subject.
gollark: And browers won't recognize them.
gollark: I mean, you *can* get top level domains, it's just hilariously expensive and subject to approval processes.
See also
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.