Rigidity is undecidable

Bojańczyk, Mikołaj; Szawiel, Stanisław; Zawadowski, Marek

doi:10.1017/s096012951300087x

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2014

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“…However, the problem of whether a finite set of linear-regular equations defines a rigid theory is undecidable (Bojańczyk et al 2014). The notion of a linear-regular theory was considered in universal algebra but the notion of a rigid theory, as well as that of a linear-regular interpretation, seems to be new.…”

Section: Introductionmentioning

confidence: 99%

Theories of analytic monads

Szawiel¹,

Zawadowski²

2014

Math. Struct. Comp. Sci.

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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

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Section: Introductionmentioning

confidence: 99%