Tensor Hopf endofunctor
An approach to A¥-categories presented at the book "Closed multicategory of pretriangulated A¥-categories" (joint with Volodymyr Lyubashenko and Oleksandr Manzyuk) involves construction of Kleisli multicategory for free cocategory comonad T ³ 1 on the Monoidal category of augmented graded k-linear quivers.
The talk is devoted to an observation concerning Hopf algebra structure on the endofunctor T ³ 1. We explain how bialgebra projection appear in the construction of A¥-analog of Verdier factor-category. Finally, we discus some new constructions from higher dimensional algebra that concern the matter.