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nLab > Latest Changes: VectBund

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022
    • (edited Nov 21st 2022)

    starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base BB).

    For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2023
    • (edited Apr 5th 2023)

    added (here) a section “Properties — Distributive monoidal structure” which spells out the elementary argument that (Vect Set,⊔,⊠)(Vect_{Set}, \sqcup, \boxtimes) is distributive monoidal (a verbatim copy of the same few paragraphs which I just added at distributive monoidal category, announed there)

    also added (here) a further subsection “Properties — Amalgamation of monoidal and parameter structures” which is meant to be experimental for the moment (I left a disclaimer “under construction”).

    The point of this last subsection I discuss in another thread: here.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2023

    added a line (here) on the bireflective inclusion of zero-bundles

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorperezl.alonso
    • CommentTime34 minutes ago

    When does this category have equalizers preserved by the tensor product? I imagine that’s when the category of base spaces satisfies the same condition?

1 to 4 of 4

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