Algebraic weak factorisation systems I: accessible AWFS

John Bourke, Richard Garner*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    32 Citations (Scopus)


    Algebraic weak factorisation systems (awfs) refine weak factorisation systems by requiring that the assignations sending a map to its first and second factors should underlie an interacting comonad-monad pair on the arrow category. We provide a comprehensive treatment of the basic theory of awfs-drawing on work of previous authors-and complete the theory with two main new results. The first provides a characterisation of awfs and their morphisms in terms of their double categories of left or right maps. The second concerns a notion of cofibrant generation of an awfs by a small double category; it states that, over a locally presentable base, any small double category cofibrantly generates an awfs, and that the awfs so arising are precisely those with accessible monad and comonad. Besides the general theory, numerous applications of awfs are developed, emphasising particularly those aspects which go beyond the non-algebraic situation.

    Original languageEnglish
    Pages (from-to)108-147
    Number of pages40
    JournalJournal of Pure and Applied Algebra
    Issue number1
    Publication statusPublished - 1 Jan 2016


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