Abstract
A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained intro- duction to the theory of Hopf monoids in the category of species. Combinato- rial structures which compose and decompose give rise to Hopf monoids. We study several examples of this nature. We emphasize the central role played in the theory by the Tits algebra of set compositions. Its product is tightly knit with the Hopf monoid axioms, and its elements constitute universal op- erations on connected Hopf monoids. We study analogues of the classical Eulerian and Dynkin idempotents and discuss the Poincare-Birkhoff-Witt and Cartier-Milnor-Moore theorems for Hopf monoids.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
