Categorifying rationalization

Clark Barwick, Saul Glasman, Marc Hoyois, Denis Nardin, Jay Shah

Research output: Contribution to journalArticlepeer-review


We solve a problem proposed by Khovanov by constructing, for any set of primes S, a triangulated category (in fact a stable ∞-category) whose Grothendieck group is S−1Z. More generally, for any exact ∞-category E, we construct an exact ∞-category S−1E of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this ∞-category is precisely the result of categorifying division by the primes in S. In particular, Kn(S−1E) ∼= S−1 Kn(E).
Original languageEnglish
Number of pages15
JournalForum of Mathematics, Sigma
Issue number42
Early online date9 Jan 2020
Publication statusE-pub ahead of print - 9 Jan 2020


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