Category theory is a field of mathematics that studies relationships between structures. Meta Object Facility (MOF) is a language for designing metamodels whose structures are made of classes and relationships. This paper examines how key categorical concepts such as functors and natural transformations can be used for equational reasoning about modeling artifacts (models, metamodels, transformations). This leads to a formal way of specifying equivalence between models, and offers many practical applications including refactoring and reasoning.