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In "BASIC CONCEPTS OF ENRICHED CATEGORY THEORY", (version Reprints in Theory and Applications of Categories, No. 10, 2005), chapter 4.7 p.75-76, Kelly introduces the "discrete Grothendieck construction" in the case V=Set, and says that he'll treat the cases V=Gpd and V=Cat in an article "[46] G.M. Kelly, Categories with structure – biadjoints for algebraic functors, to appear."

I can't find this article under that name, does anyone have a reference for this?

Thanks!

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  • $\begingroup$ A relevant paper is "Two-dimensional monad theory" by Blackwell, Kelly and Power. Theorem 5.12 of that paper certainly gives an important result on biadjoints for algebraic functors. $\endgroup$
    – john
    Apr 25, 2016 at 11:58
  • $\begingroup$ The paper in question never appeared; see list of category theory papers that never appeared. $\endgroup$
    – varkor
    Nov 7, 2023 at 12:05

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The name of that article changed (a lot, it seems): the information you seek is in the paper Doctrinal Adjunction by Kelly. It lies on page 257 of the collection

Category Seminar, Number 420 of Lecture Notes in Mathematics, Springer-Verlag (1974).

You can at least sample the first few pages of the article here.

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  • $\begingroup$ This is a different paper: both "Categories with structure – biadjoints for algebraic functors" and "Doctrinal adjunction" are referenced separately in Basic Concepts of Enriched Category Theory. $\endgroup$
    – varkor
    Nov 7, 2023 at 12:04

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