Ok if research time is what you are concerned about that is lowered by passives in each of the skills that require trait research (provisioning alchemy and enchanting not needing research)
If inspiration is what you’re asking it falls is the skill you used(blacksmith effects blacksmith) and is used to get you to level 50 in these skills
This is off the top of my head at work so I might have got something bass ackwards but you will probably get more answers

Research time is lowered only by the passives, and each affects only the one skill's research. Orcs' bonus to inspiration lets them get the passive sooner, but doesn't affect the research directly.

Inspiration gained is applied directly to the skill and there's no cross-skill benefits. The only place where skills combine is furnishing, where an item requires multiple skills to craft it.

fetito666 wrote: »

So inspiration only increased the crafting level, but it does not decrease the research time?

So inspiration is basically XP for the crafting skill?

yes, exactly.