I've played the same save of Pocket Card Jockey on my DS for years now, picking the game up any time I know I'll have some time to kill and putting it back down when I realize I have to do other things like eat and sleep.
Horses have different characteristics and skills, which can be passed to their offspring. However, inbreeding results in poor-temper horses. I think that you can balance those needs but have mostly been trying to avoid inbreeding as a matter of course.
My problem arises in forgetting what I was doing when I last took a breath to walk amongst the living. The in-game menu is not the most intuitive and the game's fandom is on the small side, meaning documentation is thin.
I have avoided, so far, creating any sort of spreadsheet to track this because sometimes I am aware of what restraint looks like. Is there an in-game way to see a horse's ancestors so I can avoid inbreeding without meticulous out-of-game notes?