(0,1)-category theory: logic, order theory

(0,1)-category

relation between preorders and (0,1)-categories

proset, partially ordered set (directed set, total order, linear order)

top, true,

bottom, false

monotone function

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

A poset is Noetherian if every ascending chain of ideals (sieves) stabilizes, and it is co-Notherian if every ascending chain of ideals in the opposite poset stabilizes.

Last revised on May 6, 2022 at 05:20:58. See the history of this page for a list of all contributions to it.