So in trying to make my own notes for things, I wanted to make use of the word "classifications". Not the act of classification, but rather the plural of the idea of "a classification", as in, "Animals are a classification of living things". As I see it, it's similar to using the word class, group or category, but I find it carries less of an objective connotation. Kind of like saying 数学的 instead of 数理的. Both mean "mathematical", but the former is mathematical within the scope of our study of math, whereas the latter seems to encompass things beyond the scope of our study (ex. 数理的思考、the idea of mathematical thinking, see https://www.kitasato-u.ac.jp/sci/resea/buturi/hisenkei/sogo/suuri.pdf).
So back to the point, the main words I've been able to find that relate to classification are 分類、類別 and 部類. The former two seem to imply the act of classification as far as I can see, and I don't know if they can be used the way I'm looking to use classification. As for 部類, it looks at first glance that it's similar to class/group/category, with the more objective connotation. Maybe the lines are blurred in translation, but is there any word more specific to what I'm looking for? Can't find one myself.