Algebraic Weak Factorisation Systems I: Accessible Awfs

@inproceedings{Bourke2014AlgebraicWF,
  title={Algebraic Weak Factorisation Systems I: Accessible Awfs},
  author={John Bourke and Richard Garner},
  year={2014}
}
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… CONTINUE READING

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