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I want to ask a stupid question. I wonder whether following morphism exists in general

Let I be an infinite set. i belongs to I

Hom(A,colimBi)--->limHom(A,Bi) and

ColimHom(A,Bi)---->Hom(A,colimBi)

What I know is if we replace lim by infinite product and colim by infinite coproduct. It exists,but I am not sure in this general case above

I want to ask a stupid question. Let $I$ be an infinite set and suppose $i$ belongs to $I$. I wonder whether following morphisms exist in general:

Hom($A$,colim $B_i) \to$ lim Hom($A,B_i$) and

Colim Hom($A,B_i) \to$ Hom($A$,colim $B_i$)

What I know is: if we replace lim by infinite product and colim by infinite coproduct, it exists. But I am not sure in this general case above.

I want to ask a stupid question. I wonder whether following morphism exists in general

Let I be an infinite set. i belongs to I

Hom(A,colimBi)--->limHom(A,Bi) and

Colim(A,B1)---->Hom(A,colimBi)

What I know is if we replace lim by infinite product and colim by infinite coproduct. It exists,but I am not sure in this general case above

I want to ask a stupid question. I wonder whether following morphism exists in general

Let I be an infinite set. i belongs to I

Hom(A,colimBi)--->limHom(A,Bi) and

ColimHom(A,Bi)---->Hom(A,colimBi)

What I know is if we replace lim by infinite product and colim by infinite coproduct. It exists,but I am not sure in this general case above