Descent and duality

Annals of Pure and Applied Logic 71 (2):131-188 (1995)
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Using the Makkai's duality for first-order logic, we characterise effective descent morphisms in 2-categories of pretoposes and Barr-exact categories. In both cases they coincide with conservative morphisms. We show that in those 2-categories the 2-coregular factorisations are exactly quotient-conservative factorisations. We also prove a generalisation of the Makkai duality for pseudoelementary categories



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Definability and descent.David Ballard & William Boshuck - 1998 - Journal of Symbolic Logic 63 (2):372-378.

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Strong conceptual completeness for first-order logic.Michael Makkai - 1988 - Annals of Pure and Applied Logic 40 (2):167-215.

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