A categorification of the square root of $-1$
Volume 232 / 2016
Fundamenta Mathematicae 232 (2016), 89-98
MSC: Primary 18D10; Secondary 16G20, 16D20.
DOI: 10.4064/fm232-1-7
Abstract
We give a graphical calculus for a monoidal DG category $\mathcal {I}$ whose Grothendieck group is isomorphic to the ring $\mathbb {Z}[\sqrt {-1}]$. We construct a categorical action of $\mathcal {I}$ which lifts the action of $\mathbb {Z}[\sqrt {-1}]$ on $\mathbb {Z}^2$.
