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Lax descent theorems for left exact categories

Abstract We study the 2-category of categories with finite limits, Lex. We characterise descent, effective descent and chain descent morphisms. These classes of morphisms do not coincide in Lex. We also study relations between these and other naturally arising classes of conservative morphisms. We define, in a semantical way, a new false quotient-strongly conservative factorisation in Lex. We prove that the iteration of the descent construction eventually "stops" at this factorisation....

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