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Is the gluing of bundles from not-necessarily trivial bundles just some kind of 2-colimit?

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Gluing is an ordinary colimit, so you can certainly think of it as "some kind of 2-colimit", if you really believe that helps you. –  Johannes Ebert Mar 10 '12 at 16:09
    
Johannes is right. What you might be thinking is, the category of principal bundles over a fixed base is a $2$-colimit over all covers of the base (or some cofinal subset) of the categories of principal bundles over that fixed base which trivialize over the given cover. –  David Carchedi Mar 13 '12 at 12:45
    
@Carchedi: I wasn't actually ;), but after Johannes comment I realised he was right but I still felt there was a 2-colimit involved somewhere but was struggling to make the statement clear. Thanks for clarifying. –  Mozibur Ullah Mar 14 '12 at 12:30

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not my answer, but David Carchedi's answer in a comment:

'What you might be thinking is, the category of principal bundles over a fixed base is a 2-colimit over all covers of the base (or some cofinal subset) of the categories of principal bundles over that fixed base which trivialize over the given cover'

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