2021/02/22 by Hofstra, Pieter, Parker, Jason, Scott, Philip J.
#Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2102.11081
We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant isotropy group) associated with an algebraic theory to the wider class of quasi-equational theories. We apply this characterization to prove that the isotropy group of a strict monoidal category is precisely its Picard group of invertible objects. Furthermore, we obtain an explicit description of the covariant isotropy group of a presheaf category.