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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 27th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Peter Hilton]], [[Urs Stammbach]], Section I.9 in: _A course in homological algebra_, Springer-Verlag, New York, 1971, Graduate Texts in Mathematics, Vol. 4 ([doi](https://link.springer.com/book/10.1007/978-1-4419-8566-8), [pdf](https://web.math.rochester.edu/people/faculty/doug/otherpapers/hilton-stammbach.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/injective+envelope/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/injective+envelope/14">v14</a>, <a href="https://ncatlab.org/nlab/show/injective+envelope">current</a>

   added pointer to:

   • Peter Hilton, Urs Stammbach, Section I.9 in: A course in homological algebra, Springer-Verlag, New York, 1971, Graduate Texts in Mathematics, Vol. 4 (doi, pdf)

   diff, v14, current

2. • CommentRowNumber2.
   • CommentAuthorSeth Chaiken
   • CommentTimeAug 7th 2022
   • PermaLink
   Author: Seth Chaiken
   Format: MarkdownItexIt looks like injective hull is synonymous with injective envelope. The article uses hull as the "primary" word, and then has (envelope), but injective envelop is the title. How can both forms be put into the title?

   It looks like injective hull is synonymous with injective envelope. The article uses hull as the “primary” word, and then has (envelope), but injective envelop is the title. How can both forms be put into the title?

3. • CommentRowNumber3.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeFeb 17th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexLinked new page for [[Field]], the [[category]] of [[fields]]. Also linked [[fields]]. <a href="https://ncatlab.org/nlab/revision/diff/injective+envelope/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/injective+envelope/16">v16</a>, <a href="https://ncatlab.org/nlab/show/injective+envelope">current</a>

   Linked new page for Field, the category of fields. Also linked fields.

   diff, v16, current

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 28th 2024
   • (edited Jun 28th 2024)
   • PermaLink
   Author: zskoda
   Format: MarkdownItex* J.Ad&#225;mek, H. Herrlich, J. Rosick&#253, W. Tholen _Injective hulls are not natural_, Algebra univers. 48 (2002) 379--388 [pdf](https://link.springer.com/content/pdf/10.1007/s000120200006.pdf) [ps](http://www.iti.cs.tu-bs.de/~adamek/injective.hulls.AHRT.ps) I added the publication data; the previous preprint postscript link is left as well but it seems not to work. <a href="https://ncatlab.org/nlab/revision/diff/injective+envelope/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/injective+envelope/17">v17</a>, <a href="https://ncatlab.org/nlab/show/injective+envelope">current</a> P.S. [[Jiří Adámek]], [[Horst Herrlich]], [[Jiří Rosický]], [[Walter Tholen]], _Injective hulls are not natural_, Algebra univers. 48 (2002) 379--388 [doi](https://doi.org/10.1007/s000120200006)

   • J.Adámek, H. Herrlich, J. Rosick&#253, W. Tholen Injective hulls are not natural, Algebra univers. 48 (2002) 379–388 pdf ps

   I added the publication data; the previous preprint postscript link is left as well but it seems not to work.

   diff, v17, current

   P.S. Jiří Adámek, Horst Herrlich, Jiří Rosický, Walter Tholen, Injective hulls are not natural, Algebra univers. 48 (2002) 379–388 doi

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJun 29th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItex* Given a ring $R$, the category $R-Mod$ of left $R$-modules has an injective envelope. Moreover, every essential monomorphism whose domain is an injective $R$-module is an isomorphism. Injective envelope of $M$ is a terminal object in a subcategory of the undercategory $M/R-Mod$ consisting of essential morphisms (these terminal objects are called maximal essential extensions). <a href="https://ncatlab.org/nlab/revision/diff/injective+envelope/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/injective+envelope/18">v18</a>, <a href="https://ncatlab.org/nlab/show/injective+envelope">current</a>

   • Given a ring $R$, the category $R-Mod$ of left $R$-modules has an injective envelope. Moreover, every essential monomorphism whose domain is an injective $R$-module is an isomorphism. Injective envelope of $M$ is a terminal object in a subcategory of the undercategory $M/R-Mod$ consisting of essential morphisms (these terminal objects are called maximal essential extensions).

   diff, v18, current