Understanding the Small Object Argument |
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Authors: | Richard Garner |
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Institution: | (1) Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden |
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Abstract: | The small object argument is a transfinite construction which, starting from a set of maps in a category, generates a weak
factorisation system on that category. As useful as it is, the small object argument has some problematic aspects: it possesses
no universal property; it does not converge; and it does not seem to be related to other transfinite constructions occurring
in categorical algebra. In this paper, we give an “algebraic” refinement of the small object argument, cast in terms of Grandis
and Tholen’s natural weak factorisation systems, which rectifies each of these three deficiencies.
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Keywords: | Weak factorisation system Small object argument |
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