# The Catalan monoid C_5 is inherently nonfinitely based relative to finite J-trivial semigroups.

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Recall that a finite semigroup S is said to be inherently nonfinitely based (INFB) if S does not belong to any finitely based locally finite variety. In 1987, Mark Sapir proved that the 6-element Brandt monoid B_2^1 is INFB; later he gave an algorithmically efficient description of INFB semigroups. Sapir's description implies, in particular, that no finite J-trivial semigroup is INFB.