Theories of analytic monads

Details Theories of analytic monads Theories of analytic monads

2012-04-12

arxiv.org/abs/1204.2703v1

Mathematics

Category Theory

30 pages

Scientific paper

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.

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