Not signed in (Sign In)

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

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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).

nLab > Latest Changes: Mod

Bottom of Page

1 to 11 of 11

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2010

    created Mod

    • CommentRowNumber2.
    • CommentAuthorHarry Gindi
    • CommentTimeMar 19th 2010

    Question: How is this different from Ab?

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeMar 19th 2010

    Ab is the fibre over the ring of integers.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 19th 2010

    I added that remark to the entry now.

    • CommentRowNumber5.
    • CommentAuthorHarry Gindi
    • CommentTimeMar 19th 2010
    • (edited Mar 19th 2010)

    Oh, by the way, a morphism of pairs of rings and modules (R,M) -> (S,N) the way you described is called a dihomomorphism (dihomomorphisme) on the first page of EGA I. Also, what you added made it easier to understand. Thanks!

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeMar 19th 2010

    @Urs I think you will find that the observation of Quillen is actually referenced in Quillen's paper to Beck's thesis. It should be if it is not, as Jon Beck looked at the Abelianisation in that case. (Come to think of it it may be even earlier in Grothendieck Catégories cofibrées additives? I would have to check dates and content.)

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2012
    • (edited Sep 11th 2012)

    added to Mod in the section RMod is an abelian category more of the elementary details of the various statements there.

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeAug 31st 2022
    • (edited Aug 31st 2022)

    I feel that the entry Mod should be about modules/presheaves over a ringoid = small preadditive category (covariant or contravariant functors into the category of abelian groups).

    Namely, all theorems written there seem at my glance to apply to this general (and still quite standard even in pre-POV literature). The only thing specific of the category Mod R for a ring R as opposed to a ringoid is that it has a finitely generated projective generator, what does not seem to be on the page.

    7: abelianess as well as Ab3,4,5,6 (and duals of those) properties hold for an additive functor category if they hold for the codomain category. So it is quickest to notice that it holds for the category of abelian groups.

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeAug 31st 2022

    It would make more sense to me for this page to be about the monads and (bi)modules construction (properly viewed as a virtual double category), which generalises the setting on the page currently.

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeAug 31st 2022

    But this is quite a different subject with different theorems. It is about which theorems hold not about the definition.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2023

    added pointer to:

    (here and in related entries)

    diff, v30, current

1 to 11 of 11

  1.