The small object argument is a method for transfinitely constructing weak factorization systems originally motivated by homotopy theory. We establish a variant of the small object argument that is enriched over a cofibrantly generated weak factorization system. This enriched variant of the small object argument subsumes the ordinary small object argument for categories and also certain variants of the small object argument for 2-categories, (2,1)-categories, dg-categories and simplicially enriched categories.
Keywords: enriched category, small object argument, weak factorization system, copower, Day convolution, actegory
2020 MSC: 18D20, 18N40
Theory and Applications of Categories, Vol. 44, 2025, No. 16, pp 439-473.
Published 2025-05-22.
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