Is the category of class of all sets a concrete category? Since the class of all sets is not a set but is  a class, is the category of  class of all sets a concrete category?
(the only object is the class of all sets)

A concrete category is a category with a faithful functor to Set, right? And faithful means that it is injective on the hom-sets for every pair of objects.
Seeing as the category with Set as the only object and the identity as the only arrow only has one hom-set, with one element, we can just map it to a singleton set $*$, and map the identity $1_\textbf{Set}$ to the identity $1_*$. And so the answer is yes!
