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The Existential Completion
Theory and applications of categories, Tome 35 (2020), pp. 1576-1607 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and that the 2-category of existential doctrines is isomorphic to the 2-category of algebras for this 2-monad. We also show that the existential completion of an elementary doctrine is again elementary. Finally we extend the notion of exact completion of an elementary existential doctrine to an arbitrary elementary doctrine.

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Classification : 18C10, 18C15, 18D05
Keywords: existential completion, doctrines, property-like monad, tripos 
@article{TAC_2020_35_a42,
     author = {Davide Trotta},
     title = {The {Existential} {Completion}},
     journal = {Theory and applications of categories},
     pages = {1576--1607},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a42/}
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Davide Trotta. The Existential Completion. Theory and applications of categories, Tome 35 (2020), pp. 1576-1607. http://geodesic.mathdoc.fr/item/TAC_2020_35_a42/