2021/07/08 by Ford, Chase, Milius, Stefan, Schröder, Lutz · 1 citation
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.03880
We introduce a framework for universal algebra in categories of relational structures given by finitary relational signatures and finitary or infinitary Horn theories, with the arity λ of a Horn theory understood as a strict upper bound on the number of premisses in its axioms; key examples include partial orders (λ=ω) or metric spaces (λ=ω1). We establish a bijective correspondence between λ-accessible enriched monads on the given category of relational structures and a notion of λ-ary algebraic theories (i.e. with operations of arity