A new Frobenius exact structure on the category of complexes

Abstract

Let $(1)$ be an automorphism on an additive category $\mathcal{B}$, and let $\eta :(1)\to {\mathrm{Id}}_{\mathcal{B}}$ be a natural transformation satisfying ${\eta }_{X(1)}={\eta }_X(1)$ for any object $X$ in $\mathcal{B}$. We construct a new Frobenius exact structure on the category of complexes in $\mathcal{B}$, which is associated to the natural transformation $\eta$. As a consequence, the category introduced in Definition 2.4 of [J. Rickard, Morita theory for derived categories, J. London Math. Soc. 39(1989), 436-456] has a Frobenius exact structure.

15 pages

References in corpus (1)

• Three results on Frobenius categories