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On The Existence Of Category Bicompletions

Published 28 Sep 2009 in math.CT and math.AC | (0909.5010v1)

Abstract: A completeness conjecture is advanced concerning the free small-colimit completion P(A) of a (possibly large) category A. The conjecture is based on the existence of a small generating-cogenerating set of objects in A. We sketch how the validity of the result would lead to the existence of an Isbell-Lambek bicompletion C(A) of such an A, without a "change-of-universe" procedure being necessary to describe or discuss the bicompletion.

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