Title: Congruence lattices of finite diagram monoids,
Abstract: We give a complete description of the congruence lattices of the following
finite diagram monoids: the partition monoid, the planar partition monoid, the
Brauer monoid, the Jones monoid (also known as the Temperley-Lieb monoid), the
Motzkin monoid, and the partial Brauer monoid. All the congruences under
discussion arise as special instances of a new construction, involving an ideal
I, a retraction I->M onto the minimal ideal, a congruence on M, and a normal
subgroup of a maximal subgroup outside I.