Non-trivially associated tensor categories and left coset representatives

In this talk I will motivate and describe a generalisation of the group dou blecross product construction, involving a set of coset representatives for the left action of a subgroup on a group. From this data a non-trivially a ssociated tensor category can be made. I shall briefly mention the correspo nding double construction, which gives a non-trivially associated braided t ensor category, containing a braided Hopf algebra.