  General coherence theorems are constructed that yield explicit presentations
of categorical and algebraic objects. The categorical structures involved are
finitary discrete Lawvere 2-theories, though they are approached within the
language of term rewriting theory. Two general coherence theorems are obtained.
The first applies to terminating and confluent rewriting 2-theories. This
result is exploited to construct systematic presentations for the higher
Thompson groups and the Higman-Thompson groups. The presentations are
categorically interesting as they arise from higher-arity analogues of the
Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the
classical binary axioms. The second general coherence theorem holds for
2-theories that are not necessarily confluent or terminating and is used to
construct a new proof of coherence for iterated monoidal categories, which
arise as categorical models of iterated loop spaces and fail to be confluent.
