LAUSR

Abstract We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Hopf algebra H, we give an explicit description of categorical cointegrals of the category M H of left H-modules in terms of cointegrals on H. Provided that H is unimodular, we also express the Frobenius structure of the ‘adjoint algebra’ in the Yetter-Drinfeld category Y H H D by using an integral in H and a cointegral on H. Finally, we give a description of the twisted module trace for projective H-modules in terms of cointegrals on H.