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- W4320165593 abstract "In 1990, Johnstone gave a syntactic characterisation of the equational theories whose associated varieties are cartesian closed. Among such theories are all unary theories -- whose models are sets equipped with an action by a monoid M -- and all hyperaffine theories -- whose models are sets with an action by a Boolean algebra B. We improve on Johnstone's result by showing that an equational theory is cartesian closed just when its operations have a unique hyperaffine-unary decomposition. It follows that any non-degenerate cartesian closed variety is a variety of sets equipped with compatible actions by a monoid M and a Boolean algebra B; this is the classification theorem of the title." @default.
- W4320165593 created "2023-02-13" @default.
- W4320165593 creator A5045461807 @default.
- W4320165593 date "2023-02-08" @default.
- W4320165593 modified "2023-09-23" @default.
- W4320165593 title "Cartesian closed varieties I: the classification theorem" @default.
- W4320165593 doi "https://doi.org/10.48550/arxiv.2302.04402" @default.
- W4320165593 hasPublicationYear "2023" @default.
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