A construction of a quotient tensor category
| dc.creator | Hai, Phung Ho | |
| dc.date | 2006-03-12 | |
| dc.date | 2008-04-06 | |
| dc.date.accessioned | 2026-07-07T09:30:16Z | |
| dc.date.available | 2026-07-07T09:30:16Z | |
| dc.description | For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is the category of finite dimensional representations of a groupoid scheme $G$ over $k$, then $Q$ is equivalent to the representation category of a normal subgroupoid scheme of $G$. We describe such a quotient in terms of the subcategory $S$ of $T$ consisting of objects which become trivial in $Q$. We show that, under some condition on $S$, $Q$ is uniquely determined by $S$. If $S$ is an 'etale finite tensor category, we show that the quotient of $T$ by $S$ exists. In particular we show the existence of the base change of $T$ with respect to finite separable field extensions. As an application, we obtain a condition for the exactness of sequences of groupoid schemes in terms of the representation categories. | |
| dc.description | an error in Theorem 4.15 is corrected | |
| dc.identifier | https://arxiv.org/abs/math/0603279 | |
| dc.identifier | http://arxiv.org/abs/math/0603279 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158073 | |
| dc.subject | Representation Theory | |
| dc.subject | Category Theory | |
| dc.title | A construction of a quotient tensor category | |
| dc.type | text |