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math.CT2025
A constructive approach to the double-categorical small object argument
Benno van den Berg, John Bourke, Paul Seip
Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construc…
math.CT2024
The Frobenius equivalence and Beck-Chevalley condition for Algebraic Weak Factorisation Systems
Wijnand van Woerkom, Benno van den Berg
If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed u…