Many proofs and constructions now exist of Krohn–Rhodes decompositions (e.g., [Krohn, Rhodes & Tilson 1968], [Ésik 2000], [Diekert et al. 2012]), with the holonomy method the most popular and efficient in general (although not in all cases). Owing to the close relation between monoids and categories, a version of the Krohn–Rhodes theorem is applicable to category theory. This observation and a proof of an analogous result were offered by Wells (1980).See also (Tilson 1989)
