PS

Lattice

Lattice

Has all finite products(meet, infimum)かつ、has all finite coproducts(join, supremum)なposetal category。

Bounded lattice

Terminal object(greatest element)とinitial object(least element)を持つlattice。

Heyting algebra

Has all exponentialsなbounded lattice。直観論理と本質的に等しい。

命題

  •  {} ^ \forall P : \text{lattice},
    •  P: \text{complete} \Leftrightarrow P: \text{has all small products and coproducts}

参考文献