Algebraic weak factorisation systems I: Accessible AWFS☆
By John Bourke, Richard Garner. 2014
70 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c096c395b631b3cd1a0e7762e4a57b948604203c
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Frobenius condition, right properness, and uniform fibrations (2015, background): “A related, but different, approach to generating an awfs (C, Ft) from a class of monomorphisms is taken in [7].”