B with F fJ.
Perm H send each h to left multiplication lph by h, while lp~ = a~llpha. Then lp
Using only small sets and all classes one can describe many of the needed categories - in particular, our categories Set, Grp, etc. are proper classes, hence are large categories in this sense. Initially, category theory was restricted to the study of small and large categories (and based on the G6del-Bernays axioms). However, we will have many occasions to form categories which are not classes. One such is the category Cis of all classes: Its objects are all classes; its arrows all functions f : C ---+ C' between classes.