一句话：证明 CABA 上某自函子的代数范畴与 Set 上幂集余代数范畴对偶，并由 Tarski 对偶推出 Thomason 对偶。
论文研究 Set 上幂集自函子 P 的余代数范畴 Coalg(P) 的对偶理论。作者首先证明从完全原子布尔代数与完全布尔同态构成的范畴 CABA 到完全交半格与完全交同态构成的范畴 CSL 的遗忘函子具有左伴随。借助该伴随，他们在 CABA 上构造自函子 H，使得 H-代数范畴 Alg(H) 与 Coalg(P) 对偶等价。作为推论，作者由 Tarski 对偶推导出 Thomason 对偶，这与 Jónsson-Tarski 对偶可由 Stone 对偶推导的方式相平行。该工作用范畴论与余代数方法统一了若干对偶性。
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.