  We define a concept which we call multiplicity. First, multiplicity of a
morphism is defined. Then the multiplicity of an object over another object is
defined to be the minimum of the multiplicities of all morphisms from one to
another. Based on this multiplicity, we define a pseudo distance on the class
of objects. We define and study several multiplicities in the category of
topological spaces and continuous maps, the category of groups and
homomorphisms, the category of finitely generated $R$-modules and $R$-linear
maps over a principal ideal domain $R$, and the neighbourhood category of
oriented knots in the 3-sphere.
