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    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 25th 2018

    The inductive tensor product is the analogue of the projective tensor product where we have a universal property wrt separately continuous maps. For Fréchet spaces they agree.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 25th 2018

    Added floating toc and contents.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 25th 2018

    added a bunch of hyperlinks to various technical terms in the first few paragraphs. in particular I made sure that there are links back to tensor product and tensor product of vector spaces. Conversely, I made these entries also point to inductive tensor product

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 30th 2018

    Added original reference to Grothendieck’s nuclear spaces monograph, added theorem about further properties: the tensor product commutes with inductive limits and makes lctvslctvs a symmetric monoidal closed category.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 30th 2018

    Is this result about lctvs as a closed symmetric monoidal category due to Grothendieck?

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 30th 2018
    • (edited May 30th 2018)

    Not sure. I saw it in Ralf Meyer’s book on cyclic homology, but it was a throwaway comment, together with the complaint that it’s not very useful, due to the problem with the completed inductive tensor.

    Sydow, in On hom-functors and tensor products of topological vector spaces, dating from 1982, says “it is is easy to see”.

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 30th 2018

    Andrew Stacey talks through the issue in this comment (and following) from ten or so years ago. He refers to this book for details.

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