1. In a monoid category M describe, with reasons, the identity arrow, monomorphisms, epimorphisms and isomorphisms. Qn 2. Let A and B be categories. Consider the product category A x B defined as follows: 1) (A, B) is an object in A x B iff A is an object in A and B is an object in B. (f,g) f 2) (A, B) (A', B') is a morphism in A x B iff A A' is an A-arrow and B is a B-arrow. [9] B' (i) Specify the identity arrows and compositions in A x B. (ii) Prove the following statement: (f, g) is a monomorphism in A x B iff f is an monomorphism in A and g is an monomor- phism in B. [8] [3,4]