nLab involutive poset

Definition

An involutive poset is a poset $P$ with an antitonic involution $\neg:P \to P$.

Finite involutive posets

The category of finite involutive posets is the opposite category of the category of finite De Morgan algebras, with dualising object $\mathbb{2}^\mathbb{2}$. The category of finite involutive posets is also the opposite category of the category of finite Kleene algebras, with dualising object $\mathbb{3}$.

Related concepts

• De Morgan algebra

• Kleene algebra

• poset

• involution

References

• William H Cornish, Peter R Fowler, Coproducts of de morgan algebras, Bulletin of the Australian Mathematical Society, 16(01):1–13, 1977. (pdf)

• William H Cornish, Peter R Fowler, Coproducts of kleene algebras, Journal of the Australian Mathematical Society (Series A), 27(02):209–220, 1979 (pdf)

• Bas Spitters, Cubical sets and the topological topos (arXiv:1610.05270)