Algebraic Weak Factorisation Systems I: Accessible Awfs

  title={Algebraic Weak Factorisation Systems I: Accessible Awfs},
  author={John Bourke and Richard Garner},
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


Publications referenced by this paper.
Showing 1-10 of 51 references

Monoidal Algebraic Model Structures

View 5 Excerpts
Highly Influenced

Natural Weak Factorization Systems

View 4 Excerpts
Highly Influenced

Algebraic weak factorisation systems II: weak maps

J. Bourke, R. Garner
Preprint, available as arXiv:1412.6560, • 2014
View 1 Excerpt

Homotopical resolutions associated to deformable adjunctions

A. J. Blumberg, E. Riehl
Algebraic & Geometric Topology 14, • 2014
View 1 Excerpt

Quasi-categories, profunctors and equipments

D. Verity
Talk to Australian Category Seminar, • 2014
View 1 Excerpt

Similar Papers

Loading similar papers…