This paper aims to bring the benefits of the use of Category Theory to the field of Semantic Web, where the coexistence of intrinsically different models of local knowledge makes difficult the exchanging of information. The paper uses categorical limit and colimit to define operations of breaking and composing ontologies, formalizing usual concepts in ontologies (alignment, merge, integration, matching) and proposing a new operation (the hide operation). The presented set of operations form a useful framework that makes easier the manipulation and reuse of ontologies.