Algebraic K-Theory for Lawvere Theories: Assembly and Morita Invariance

Much like operads and monads, Lawvere theories are a way of encoding algebraic structures, such as those of modules over a ring or sets with a group action.  In this talk, we discuss the algebraic K-theory of Lawvere theories, which contains information about automorphism groups of these structures.  We'll discuss both particular examples and general constructions in the K-theory of Lawvere theories, including examples showing the limits of Morita invariance and the construction of assembly-style maps.  This is joint work with Markus Szymik.