I have been reading Gonçalo Tabuada's paper Higher K-theory via universal invariants in a seminar and the following question arose.

At one point in his construction (specifically $\S$10) he looks at the set of full dg-inclusions $\mathcal G\hookrightarrow\mathcal H$ where $\mathcal H$ is a strict finite $I$-cell, where $I$ is the usual (I suppose) set of generating cofibrations of the category dgcat of small dg-categories where we take Morita equivalences as the weak equivalences. The interest is in the Drinfeld quotient $\mathcal H\,/\,\mathcal G$.

The main question I have is the following: is this quotient still (weakly/Morita equivalent to) a strict finite $I$-cell? I'm not sure this is required for Tabuada's argument to hold, but it would be nice to know if we can take the quotient in the 'finite' part of dgcat.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.