幂集余代数的对偶性
Duality for powerset coalgebras
AI总结：
本文通过构造CABA到CSL遗忘函子的左伴随，建立幂集余代数范畴与某代数范畴的对偶等价，并由此从Tarski对偶性推导出Thomason对偶性。
摘要：
设CABA为完全原子布尔代数与完全布尔同态的范畴，设CSL为完全交半格与完全交同态的范畴。我们证明从CABA到CSL的遗忘函子存在左伴随。这使得我们能够描述CABA上的一个自函子H，使得H的代数范畴Alg(H)与集合上幂集自函子P的余代数范畴Coalg(P)对偶等价。作为推论，我们从Tarski对偶性推导出Thomason对偶性，从而与从Stone对偶性推导出Jónsson-Tarski对偶性的方式相平行。
英文摘要：
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 Jónsson-Tarski duality is derived from Stone duality.
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