Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012
    • (edited Oct 4th 2012)

    at additive functor there was a typo in the diagram that shows the preservation of biproducts. I have fixed it.

    Also formatted a bit more.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012

    Added a pointer to an old article by Watt and stated the theorem that a right exact additive functor between categories of modules comes from tensoring with a bimodule.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeOct 4th 2012
    • (edited Oct 4th 2012)

    It is Charles E. Watts, rather than Watt. Eilenberg had independently the same result.

    I have long time ago created an entry Eilenberg-Watts theorem about the right exact functors between the categories of modules over rings. Maybe this material you added on right exact functors between categories of modules should be integrated there instead. I think this is rather specific material which is not belonging really into a general entry on additive functors as the result is specific about module categories, though a short line with a remark and link to the specialized entry Eilenberg-Watts theorem makes sense. A good reference for this material are intro chapters in Bass’s book on algebraic K-theory. There are some generalizations (and dualizations) for some other setups like in some works of Pareigis, then Schauenburg and so on, in my memory.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012

    It is Charles E. Watts, rather than Watt.

    Thanks; I have fixed it. I remember thinking “Haha, it’s not drummer Charlie Watts ” …

    I have long time ago created an entry Eilenberg-Watts theorem

    Ah, thanks, I have linked to it now. (I expect there are many more entries of yours which I will never find because you don’t link to them…)

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeOct 4th 2012

    But it is linked, e.g. at the main entry abelian category.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 4th 2012
    • (edited Oct 4th 2012)

    But it is a statement about

    1. additive functors

    2. and exact functors

    3. between categories of modules.

    So to guarantee that it isn’t duplicated when somebody else comes from any of these three ingredient-entries, it should be linked to from

    1. additive functor

    2. exact functor

    3. category of modules

    (I have done that meanwhile.)

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)