What are the units for Story Points?

A co-worker and I were discussing estimation on agile software development teams (Yeah, I know - #noestimates. That was off the table here). I asked him what a story point represents. He said "effort", which PMBOK defines as "measurable work units", and pointed me to a post by Michael Cohn:

"...story points are about time—the effort involved in doing something. Because our bosses, clients and customers want to know when something will be done, we need to estimate with something based on effort. Risk, uncertainty and complexity are factors that may influence the effort involved."

My friend went on to write the following formulas:

(SumOfRemainingEpics + SumOfRemainingStories) / Velocity = Forecasted Duration (+/- uncertainty)

and

Forecasted Duration / Team Capacity = hours

I wasn't so sure that this demonstrated that story points are about time, so I re-wrote his formulas adding units (and dropping uncertainty):

SumOfRemainingEpicsAndStories(points) / Velocity(points/week) = Forecasted Duration(weeks) 

and

( (SumOfRemainingEpics(points) + SumOfRemainingStories(points)) / Velocity (points/week) ) x Team Capacity (hours/week) = hours

Management wants estimates of duration which we calculate according to the first equation by dividing points by velocity (Cohn mentions this too). In either formula, points cancel out. What that says to me is that units of story points don't matter. We can estimate in complexity, risk, time, or elephants! The upside of this is that non-timebased units for points prevents management from translating stories directly back and forth between points and hours, which can cause friction between the team and management