Let 
be a nontrivial bounded lattice (or
a complemented lattice, etc.). Then 
is a tight lattice if every proper tolerance 
of 
satisfies
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Tight lattices play an important role in the study of congruence lattices on finite algebras. One can show that a finite lattice 
is tight if and only if it is 
-simple and every strictly increasing meet endomorphism of
is constant. One can also show that
a finite lattice 
is tight if and only if its only connected tolerance is the all relation, 
.
