(a) If S D is a functor, let S) 1 if S is covariant and 1 if S is contravariant If T D is another functor, show that TS is a functor from to whose variance is given by (TS) (T)(S) (b) Generalize part (a) to any finite number of functors, S 1 1 2 , S 2 2 3 , ,S n n n 1 ...

a To show that TS is a functor from to where is the category that you have omitted we need to demonstrate that TS satisfies the two functor properties ...

(a) If S : D is a functor, let {S) = 1 if S is...

Question:

(a) If S : ℓ → D is a functor, let σ{S) = 1 if S is covariant and -1 if S is contravariant. If T: D → ℓ is another functor, show that TS is a functor from ℓ to ℇ whose variance is given by σ(TS) = σ(T)σ(S).

(b) Generalize part (a) to any finite number of functors, S₁ : ℓ₁ → ℓ₂, S₂ : ℓ₂ → ℓ₃, ... ,S_n: ℓ_n -- ℓ_n+1•