Editing Isomorphism of categories (section)

==Properties==
As is true for any notion of [[isomorphism]], we have the following general properties formally similar to an [[equivalence relation]]:
* any category ''C'' is isomorphic to itself
* if ''C'' is isomorphic to ''D'', then ''D'' is isomorphic to ''C''
* if ''C'' is isomorphic to ''D'' and ''D'' is isomorphic to ''E'', then ''C'' is isomorphic to ''E''.

A functor ''F'' : ''C'' → ''D'' yields an isomorphism of categories if and only if it is [[bijective]] on objects and on [[Hom set|morphism sets]].<ref name="catswork"/> This criterion can be convenient as it avoids the need to construct the inverse functor ''G''.