Centres of monoidal categories of functors

This paper explores when the (lax) centre of a closed monoidal (enriched) functor category is again a functor category. For some of this, we exploit the Kleisli construction in the bicategory of modules between enriched categories. We look at (lax) centres of reflective full subcategories of monoidal functor categories. A result is obtained concerning the centre of the pointwise tensor product structure on the category of functors from a groupoid to a wide class of monoidal categories.