We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

Author Bio

Dene Lepine was an undergraduate student at the University of Ottawa and will soon be a Master’s student there as well. His interests lie within Lie theory and representation theory. While he is not doing mathematics he can be found doing Brazilian Ju-Jitsu or looking for new things to learn.