7 research outputs found
Monads of regular theories
We characterize the category of monads on and the category of Lawvere
theories that are equivalent to the category of regular equational theories.Comment: 36 page
Theories of analytic monads
We characterize the equational theories and Lawvere theories that correspond
to the categories of analytic and polynomial monads on Set, and hence also the
categories of the symmetric and rigid operads in Set. We show that the category
of analytic monads is equivalent to the category of regular-linear theories.
The category of polynomial monads is equivalent to the category of rigid
theories, i.e. regular-linear theories satisfying an additional global
condition. This solves a problem A. Carboni and P. T. Johnstone. The Lawvere
theories corresponding to these monads are identified via some factorization
systems.Comment: 29 pages. v2: minor correction
Rigidity is undecidable
We show that the problem `whether a finite set of regular-linear axioms
defines a rigid theory' is undecidable.Comment: 8 page