幂集代数的对偶性

Log. Methods Comput. Sci. Pub Date : 2020-08-04 DOI:10.46298/lmcs-18(1:27)2022

G. Bezhanishvili, L. Carai, P. Morandi

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引用次数: 2

摘要

设CABA是完全原子布尔代数和完全布尔同态的范畴，CSL是完全满足半格和完全满足同态的范畴。我们证明了从CABA到CSL的遗忘函子有一个左伴随。这允许我们描述CABA上的内函子H，使得H的代数范畴Alg(H)与集合上幂集内函子P的余代数范畴Coalg(P)双等价。因此，我们从Tarski对偶中推导出Thomason对偶，从而平行于从Stone对偶中推导出J的onsson-Tarski对偶。

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Duality for powerset coalgebras

Let CABA be the category of complete and atomic boolean algebras and complete boolean homomorphisms, and let CSL be the category of complete meet-semilattices and complete meet-homomorphisms. We show that the forgetful functor from CABA to CSL has a left adjoint. This allows us to describe an endofunctor H on CABA such that the category Alg(H) of algebras for H is dually equivalent to the category Coalg(P) of coalgebras for the powerset endofunctor P on Set. As a consequence, we derive Thomason duality from Tarski duality, thus paralleling how J\'onsson-Tarski duality is derived from Stone duality.

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Log. Methods Comput. Sci.

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