Abstract
The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems (awfss) to cover some important examples that are not locally presentable categories. Secondly, to prove that cofibrantly kz-generated awfss (a notion we define) are always lax orthogonal. Thirdly, to show that the two known methods of building lax orthogonal awfss, namely cofibrantly kz-generation and the method of “simple adjunctions”, construct different awfss. We study in some detail the example of cofibrant kz-generation that yields representable multicategories, and a counterexample to cofibrant generation provided by continuous lattices.
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Communicated by M. M. Clementino.
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The author gratefully acknowledges the support of the following institutions during the long gestation of this article: a Research Fellowship of Gonville and Caius College, Cambridge; the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge; sni-anii, pedeciba and Universidad de la República.
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López Franco, I. Cofibrantly Generated Lax Orthogonal Factorisation Systems. Appl Categor Struct 27, 463–492 (2019). https://doi.org/10.1007/s10485-019-09561-1
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DOI: https://doi.org/10.1007/s10485-019-09561-1
Keywords
- Algebraic weak factorization system
- Weak factorization system
- Lax factorization system
- Multicategory
- Continuous lattice
- Orthogonal factorization system
- Cofibrant generation