Exercise 7 (Chapter 2, “Categories”): In the category of sets, the two morphisms ( and ) in a direct product are monomorphisms and the two morphisms in a direct sum are epimorphisms. Is this true in every category? There are two mistakes in this wording. The author has exchanged “monomorphisms” and “epimorphisms”. In a direct…
Chapter 12 (Functors) gives as an example of a functor the “free group functor” from the category of sets () to the category of groups (). We will call this functor , and its construction, as described, is the following: For any set , the object is the free group on . Let be a…
(Unfinished) In Chapter 12, R.G. describes three possible transformations “from real to complex vector spaces and back”. Inspired by Chapter 17 (Functors), I have examined these transformations from the functor point of view. We can distinguish not two, but three categories here, the first and third of which are equivalent: : Complex vector spaces with…