For my own future reference as much as anything else.
Based on the discussion found here, here's a list of the different sorts of cooperation with evil Catholic moral theology recognizes (he terms in red represent immoral forms of cooperation; the terms in blue represent forms of cooperation that may be moral):
Types of Cooperation
Formal: "a willing participation on the part of the cooperative agent in the sinful act of the principal agent"
Explicit Formal: the cooperative agent expresses his willingness
Implicit Formal: "even though the cooperator denies intending the wrongdoer's object, no other explanation can distinguish the cooperator's object from the wrongdoer's object"
Material: participation in a sinful act without sharing in the intent of the principal agent
Immediate Material: "the object of the moral act of the cooperator is indistinguishable from that of the principal agent;" considered morally equivalent to implicit formal cooperation
Mediate Material: "the moral object of the cooperator's act is not that of the wrongdoer's"
Proximate [Mediate] Material: the action of the cooperator is closely related to the action of the wrongdoer
Remote [Mediate] Material: the action of the cooperator is not closely related to the action of the wrongdoer
Mediate material cooperation is morally licit when there is a proportionate reason for cooperating. As I wrote below, the more proximate the cooperation, the stronger the reason must be to be proportionate.