A lattice is a poset or (0,1)-category $(P, \leq, \bot, \vee, \top, \wedge)$ such that $(P, \leq, \bot, \vee)$ is a join-semilattice and $(P, \leq, \top, \wedge)$ is a meet-semilattice

poset

join-semilattice

meet-semilattice

distributive lattice

sigma-complete lattice

suplattice

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