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for completeness: unitization
New entry unital category in the sense of Bourn. Unfortunately not much in accordance to other unitalities (in higher category theory).
I generalised unitalisation to nonassociative algebras.
Er, wait. I spent some time with renaming “unitalization” to “unitization”. You revereted it? Well, it’s fine with me if that’s more correct!
I prefer “unitalization” myself. (Cf. “abelianization”.)
Sorry Urs, I thought that “unitization” was a typo.
What happened was that first I had created the entry titled “unitalization”. Then I was going through some literature and saw it as “unitization”. So I renamed entries and everything. But never mind, you decide on what it should be called! :-)
I added a couple of observations (Remarks 3.3 and 3.4) at the section unitization of the page nonunital ring:
i) I always thought the just-so definition in terms of with the multiplication was a bit mysterious, so I pointed out that you can get the same thing by taking and quotienting out by relations which say that is a unit.
ii) The universal property of the unitalization and the fact that endomorphism rings of abelian groups are unital means that a module over a nonunital ring is the same thing as a module over its unitalization.
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