# The Subcategory of Infinite Sets

I have to show that the subcategory of infinite sets, say $$\infty$$-Set, is a full subcategory. However, is this really as simple as:

Consider two objects, A and B, in $$\infty$$-Set. Note that $$Hom_{\infty-Set}(A,B) = B^A$$. Hence, it equals $$Hom(A,B)$$ trivially.

• What is "the subcategory of infinite sets"? To define a subcategory you have to state which objects and which morphisms are in it. What do you mean by "full subcategory"? There are at least two definitions, one of which is not in common use but would require you to check a further condition. It seems to me that the exercise is just to check that you know the definitions. May 31 at 6:08
• @ZhenLin could you perhaps clarify what you mean? May 31 at 12:49