It differs from the traditional category theory in two directions : all morphisms have types and the composition of morphisms is not necessary a morphism . two aspects of application of typed category theory are discussed : cones and limits of knowledge complexity classes and knowledge completion with pseudo - functors 一個帶類型范疇是一個四元組k o , m , g , t ,其中o是一組對象, m是一組態射,每個態射有一個類型,表示f是從a到b的態射,具有類型t 。