(0,1)-category theory: logic, order theory
(0,1)-category
proset, partially ordered set (directed set, total order, linear order)
top, true,
bottom, false
implication
filter, interval
lattice, semilattice
meet, logical conjunction, and
join, logical disjunction, or
compact element
lattice of subobjects
complete lattice, algebraic lattice
distributive lattice, completely distributive lattice, canonical extension
hyperdoctrine
(0,1)-topos
Heyting algebra
regular element
Boolean algebra
frame, locale
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