Australian Category Seminar

Crossed modules give rise to monoidal categories of a special kind (groups in Cat). Braidings on these monoidal categories amount to bracket operations (like abstract commutators) on crossed modules. These arise as Samelson brackets in homotopy theory $\pi_2 X \times \pi_2 X \to \pi_3 X$. In preparation for characterizing braided monoidal groupoids with each Aq- an equivalence, aspects of group cohomology were discussed.