More on lax monoids

Ross Street – 17 October 2001

The arrival of the issue of Advances totally dedicated to [BDK] B. Bakalov, A. D'Andrea and V.G. Kac, Theory of finite pseudoalgebras, Advances in Math. 162 (2001) 1-140. caused us to append some material to our paper Brian Day and Ross Street, Lax monoids, pseudo-operads, and convolution (submitted, available electronically as pdf file). to show connections and applications of our paper to theirs. My talk concentrated on our lemma on restriction of lax promonoidal structures along a V-functor. A relevant easy example is the lax promonoidal structure on the cyclic groupoid (that is, the disjoint union of the cyclic groups). I noted that Lie algebra objects could be defined with mere cyclic symmetry. I showed how the main example of "pseudotensor category" in [BDK] fitted into a general convolution construction giving an embedding of their category into a more conventional monoidal category.