For some skills, yes, it'd make sense to have synergies. All subject to GM approval, of course.
I would try and keep crafting skills in as broad a category as possible when chosing them though, to make it clear what it is that you're learning to make.
If you pick a specific item or type of item, such as a bow or sword, I would talk with the GM when making such an item to lower the crafting DC, get a bonus or something similar to represent training in crafting a specific item. You'd never choose Craft (Sword) over Craft (Weapons) otherwise.
From memory, examples they often use of crafting skills are:
Traps
Arms
Armour
Alchemy
Leather
Carpentry
Ships
Siege Engines
Smithing
Basically, things to do with particular items or with particular materials. It'd make sense for someone who could do things with leather to make leather armour, for example, but not to me able to make Chain Mail. Likewise, a Smith could make metal armour and weapons, but not things like bows or leather armour.