The construction of a free restriction category can be broken into two steps: the construction of a free stable semilattice fibration followed by the construction of a free restriction category for this fibration. Restriction categories produced from such fibrations are `unitary', in a sense which generalizes that from the theory of inverse semigroups. Characterization theorems for unitary restriction categories are derived. The paper ends with an explicit description of the free restriction category on a directed graph.
Keywords: Restriction categories, fibrations, semigroups
2000 MSC: 18D99
Theory and Applications of Categories,
Vol. 16, 2006,
No. 15, pp 307-341.