Definition talk:Inverse Completion

There was a question asked: "Don't we need that $\left({T, \circ'}\right)$ has an identity"?

Yes it does, but this will become apparent during the course of the development of the theory. --prime mover (talk) 19:02, 1 May 2015 (UTC)

Name

Inverse completion does not seem to be easily found elsewhere but here. Involution is however and given https://www2.math.su.se/reports/2001/11/2001-11.pdf it seems to be the same construction as it provides here. And involution is more used, isn't it a better name for the process? EmperorZelos (talk) 09:41, 10 July 2020 (UTC)

The quoted document uses the term "involution" to mean the same as has been defined in Definition:Involution.

From what I've been able to piece together from the cited work, the term "involution-monoid" is what is being used for what we call an "Inverse Completion".

"Inverse Completion" is what it was called in the source work I used to create this section. I have not investigated how this is done in the various other source works I have on my shelves, but I will see what they say.

We can of course add an "also known as".

Renaming everything from "inverse completion" (which is intuitively clear as to what it means) to "involution-monoid" would be a lot of work which I'm reluctant to do (and I can bet my balls nobody else is going to be prepared to do this pointless task), so unless I'm given overwhelming evidence that the majority of the mathematical community feels the same way, along with at least one hardcopy text which backs up "involution-monoid", I'd prefer if we stuck to the terminology we have started with. --prime mover (talk) 10:56, 10 July 2020 (UTC)

Seems fair, "also known as" is a good start EmperorZelos (talk) 11:38, 15 July 2020 (UTC)