Garraway, William Dale.2014-10-2120022002AAINQ67660http://hdl.handle.net/10222/55836This work is an exploration of Supremum-enriched semicategory theory (quantaloids) and the relationship with sheaves. We begin with a review of some basic constructions and structures then introduce enriched semicategories and taxons. Next we define the category of sheaves for an involutive quantaloid Q and give an equivalence with Q -valued sets. We close by showing that a sheaf is an infimum preserving semifunctor, F : Qco → REL.Thesis (Ph.D.)--Dalhousie University (Canada), 2002.Mathematics.text