nLab weak bimonad

Idea

Weak bialgebra is like bialgebra, except that the requirement that the counit map is an algebra map and the unit is a coalgebra map are appropriately relaxed. Like bialgebras, this notion can also be properly generalized to a monoidal/bicategorical context leading to weak bimonads.

Distributive laws among monads are monads in appropriate bicategory/2-category of monads. Similarly, one can understand weak distributive laws.

Literature

• Gabriella Böhm, Stephen Lack, Ross Street, Weak bimonads and weak Hopf monads, J. Algebra 328 (2011), 1-30, arXiv:1002.4493
• Gabriella Böhm, Stephen Lack, Ross Street, On the 2-categories of weak distributive laws, Comm. Alg. 39:12 (2011) 4567–4583 doi
• Yuanyuan Chen, Gabriella Böhm, Weak bimonoids in duoidal categories, Journal of Pure and Applied Algebra 218:12 (2014) 2240–2273 doi