Limit Doctrines

Bruno Lindan

Gabriel-Ulmer duality gives a (contravariant) bi-equivalence between the 2-category Lex of finitely complete categories and that of locally finitely presentable categories.  Counterparts replacing Lex with a different 2-category of suitably complete categories fall into a general picture of dualities relative to so-called "sound" doctrines of limits.  Not every important doctrine is sound – in this talk we will investigate the extent to which unsound doctrines are able to share enough of the good properties of sound ones to admit some form of duality theorem.  

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