nLab cylinder factorisation system




A cylinder factorisation system on a category is a generalisation of a factorisation system in which we have a pair (E,M)(E, M), where EE is a class of small cocones, and MM is a class of small cones, such that every cylinder factorises uniquely as a cocone in EE followed by a cone in MM.

Cylinder factorisation systems are algebras for a pseudomonad structure given by sending each category to its Isbell envelope: see Garner 2015.


Cylinder factorisation systems were introduced in:

The special case in which EE and MM comprise classes of discrete cones was introduced in:

  • Horst Herrlich, and Walter Meyer, Factorization of flows and completeness of categories, Quaestiones Mathematicae 17.1 (1994): 1-11.

See also:

  • George E. Strecker, Flows with respect to a functor, Applied Categorical Structures 8 (2000): 559-578.

The special case in which EE is a class of epimorphisms and MM is a class of cones was studied in the following papers, including an application to colimits in categories of algebras:

Earlier still, the following considered the special case in which the right class furthermore is required to comprise discrete cones:

  • Horst Herrlich. Topological functors, General Topology and its Applications 4.2 (1974): 125-142.

See also:

  • Horst Herrlich, G. Salicrup, and R. Vazquez, Dispersed factorization structures, Canadian Journal of Mathematics 31.5 (1979): 1059-1071.

  • A. Melton, and G. E. Strecker, On the structure of factorization structures, Category Theory: Applications to Algebra, Logic and Topology Proceedings of the International Conference Held at Gummersbach, July 6–10, 1981. Springer Berlin Heidelberg, 1982.

  • Abstract and Concrete Categories

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