leading to the cup product) and from a suitable loop in the categories of extensions (leading to the Lie bracket).
We show how Schwede’s construction admits a vast generalisation to general monoidal categories with coefficients of the Ext groups taken in (weak) left and right monoidal (or Drinfel’d) centres.
In case of the category of left modules over bialgebroids and coefficients given by commuting pairs of braided (co)commutative (co)monoids in these categorical centres, we provide an explicit descri