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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 25th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexfor completeness: [[unitization]]

   for completeness: unitization

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJul 25th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexNew entry [[unital category]] in the sense of Bourn. Unfortunately not much in accordance to other unitalities (in higher category theory).

   New entry unital category in the sense of Bourn. Unfortunately not much in accordance to other unitalities (in higher category theory).

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeJul 25th 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI generalised [[unitalisation]] to nonassociative algebras.

   I generalised unitalisation to nonassociative algebras.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 25th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexEr, wait. I spent some time with renaming "unitalization" to "unitization". You revereted it? Well, it's fine with me if that's more correct!

   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!

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 27th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI prefer "unitalization" myself. (Cf. "abelianization".)

   I prefer “unitalization” myself. (Cf. “abelianization”.)

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeJul 27th 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexSorry Urs, I thought that "unitization" was a typo.

   Sorry Urs, I thought that “unitization” was a typo.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 27th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhat 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! :-)

   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! :-)

8. • CommentRowNumber8.
   • CommentAuthorjesse
   • CommentTimeSep 21st 2016
   • (edited Sep 21st 2016)
   • PermaLink
   Author: jesse
   Format: MarkdownItexI added a couple of observations (Remarks 3.3 and 3.4) at the section [[nonunital ring|unitization]] of the page [[nonunital ring]]: i) I always thought the just-so definition in terms of $A \mapsto \left(A \oplus \mathbb{Z}\right)$ with the multiplication $(a_1, z_1) \cdot (a_2, z_2) \mapsto (a_1 a_2 + a_1 z_2 + z_1 a_2, z_1 z_2)$ was a bit mysterious, so I pointed out that you can get the same thing by taking $A[x]$ and quotienting out by relations which say that $x$ 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.

   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 $A \mapsto \left(A \oplus \mathbb{Z}\right)$ with the multiplication $(a_1, z_1) \cdot (a_2, z_2) \mapsto (a_1 a_2 + a_1 z_2 + z_1 a_2, z_1 z_2)$ was a bit mysterious, so I pointed out that you can get the same thing by taking $A[x]$ and quotienting out by relations which say that $x$ 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.