There is a canonical and efficient way to extend a convergent presentation of a category by a 2-polygraph into a coherent one. Precisely, the 3-cells used in this extension procedure are in one-to-one correspondence with the confluence diagrams of critical branchings in the polygraph. Now, if the polygraph is finite, so is the set of its critical branchings, and therefore the set of 3-cells generating coherence can be taken to be finite. In such a situation, the polygraph is said to have finite derivation type, or FDT. The relevance of this concept, introduced by Squier, lies in the following invariance property: if a category admits a finite presentation having finite derivation type, then all finite presentations of also have FDT. This invariance will prove essential to show that some finitely presented categories do not admit convergent presentations. Using these conditions, Squier managed to produce an explicit example of a finitely presented monoid, with decidable word problem, but having no finite convergent presentation. This provides a negative answer to the question of universality of finite convergent rewriting.