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 beauty book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology 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 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: tensor product of abelian groups

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2012
    • (edited Aug 31st 2012)

    have split off tensor product of abelian groups from tensor product and expanded slightly

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2012

    added to tensor product of abelian groups the examples A⊗ℤ≃AA \otimes \mathbb{Z} \simeq A and ℤ a⊗ℤ b≃ℤ LCM(a,b)\mathbb{Z}_a \otimes \mathbb{Z}_b \simeq \mathbb{Z}_{LCM(a,b)}.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2012

    In the Definition-section I have made the quotient map A×B→A⊗BA \times B \to A \otimes B more explicit.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 3rd 2018
    • (edited Dec 3rd 2018)

    made notationally more explicit the forgetful functor U:Ab→SetU \colon Ab \to Set involved in declaring the universal bilinear map (here)

    diff, v9, current

  5. Removed the link as it returned 404 not found.

    Anonymous

    diff, v10, current

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 18th 2019

    Removed reference to vanished online pdf (now without link, as removed by previous editor) and replaced it by something written by Tim Gowers.

    diff, v11, current

    • CommentRowNumber7.
    • CommentAuthorYuxi Liu
    • CommentTimeJul 4th 2020

    Ab is in fact a symmetric monoidal category.

    diff, v13, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 4th 2020

    Added Whitney’s original paper.

    diff, v14, current

  9. added definition of the tensor product of abelian groups as a quotient inductive type

    Anonymous

    diff, v18, current

1 to 9 of 9

  1.