A general formalism produces directed model structures from a cylinder object, unifying the covariant and contravariant model structures on simplicial sets and the Cartesian and coCartesian model structures on marked simplicial sets.
Left determined model structures for locally presentable categories
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Covariant & Contravariant Homotopy Theories
A general formalism produces directed model structures from a cylinder object, unifying the covariant and contravariant model structures on simplicial sets and the Cartesian and coCartesian model structures on marked simplicial sets.