Abstract: Ontology alignment can solve the heterogeneity between ontology, while category theory can shield the heterogeneity between ontologies and provide uniform methodological framework for ontology integration. This paper applied category theory into the field of ontology alignment. Based on the features of gco-ontology it redefined morphism and intended to construct a more complex category, where objects are geo-ontologies, but morphism can not only express edual relationship but also describe multiple semantic relationships between geo-ontologics. Based on the definition and the features of morphism, this paper also defined ontology alignment and composing alignment, and elaborated ontology in-tcgratton.

Key words: Category theory, Morphism, Ontology alignment, Composing, Pushout