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I am looking for a reference of these, I would say, very well known facts. (strangely though finding a reference was bit trick for me).

  1. Let $C$ be a category and $F:C\rightarrow Cat$ a 2-functor in the 2-category of categories. Then the bicolimit of $F$ exists.
  2. Let $C$ be a category and $F:C\rightarrow Grpd$ a 2-functor in the 2-category of groupoids. Then the bicolimit of $F$ exists.

Has anyone got a clear reference for this?

Also, as sort of a bonus question :), if $F$ took values in groupoids, then it should not matter where we take the bicolimits, in categories or groupoids. Anyone got a reference for that fact as well?

Thank you in advance.

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  • $\begingroup$ bump. (sorry but I kinda need the references :) ). $\endgroup$
    – I.P
    Commented Jun 13, 2016 at 15:58

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