# Commit 2020-04-11 18:44 80340d83

View on Github →feat(category_theory): define action_category (#2358) This is a simple construction that I couldn't find anywhere else: given a monoid/group action on X, we get a category/groupoid structure on X. The plan is to use to use the action groupoid in the proof of Nielsen-Schreier, where the projection onto the single object groupoid is thought of as a covering map. To make sense of "stabilizer is mul_equiv to End", I added the simple fact that the stabilizer of any multiplicative action is a submonoid. This already existed for group actions. As far as I can tell, this instance shouldn't cause any problems as it is a Prop.