(a) If T D is a covariant functor, let Im T consist of the objects T(C) I C and the morphisms T() T(C) T(C ') I C C ' a morphism in Then show that Im T need not be a category (b) If the object function of T is injective, then show that Im T is a category ...

a To show that Im T need not be a category we need to find a counterexample Lets consider the following covariant functor T Set Set where Set is the c ...

(a) If T: D is a covariant functor, let Im T consist of the objects {T(C)...

Question:

(a) If T: ℓ →D is a covariant functor, let Im T consist of the objects {T(C) I C ϵ ℓ} and the morphisms {T(∫) : T(C) → T(C') I ∫: C → C' a morphism in ℓ}. Then show that Im T need not be a category.

(b) If the object function of T is injective, then show that Im T is a category.

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