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: Hmm. I may need to temporarily disable the disk-key-related features.
gollark: There is actually now the potatOS *update* signing key, which is stored on my laptop and encrypted.
gollark: It stores the key, some items, an emergency melon generator, that sort of thing.
gollark: The key is stored in some of my backup archives and Site Null on Switchcraft.
gollark: Ah yes, bruteforce a 192-bit key?
See also
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