Earlier I asked pullbacks of subsets in terms of a set of people a set of consequences, and some personal actions viewed as a function between sets, and we found out that the pullback of some subset of consequences produces the subset of people who could be responsible.
Would the same reasoning work here, expect that partition pullback takes a partition of consequences to the partition of people who could be responsible.
Also, thinking this out. The pullback of a singleton subset/partition would produce the people who were actually responsible for the singular outcome, ie if you're a murder investigator, this is the pullback you really trying to find.
Did I get this right?