In [Kimura, Math. Ann. 331: 173–201, 2005], we defined the notion of finite dimensional objects in the category of Chow motives. In this paper, we introduce the notion of finite dimensional morphisms for tensor categories so that an object is finite dimensional if and only if its identity morphism is finite dimensional. Applications to Chow motives are discussed.
© Walter de Gruyter Berlin · New York 2011