On the monad of proper factorisation systems in categories

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dc.creatorGrandis, Marco
dc.date2001-01-18
dc.date.accessioned2026-07-07T06:32:50Z
dc.date.available2026-07-07T06:32:50Z
dc.descriptionIt is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the "squaring" monad in Cat. We show in this note that an analogous fact holds for proper (i.e., epi-mono) factorisation systems and a suitable quotient of the former monad, deriving from a construct introduced by P. Freyd for stable homotopy. Structural similarities of the previous monad with the path endofunctor of topological spaces are considered.
dc.description8 pages. Key Words: Factorisation systems, 2-monads, Eilenberg-Moore algebras, pseudo algebras
dc.identifierhttps://arxiv.org/abs/math/0101154
dc.identifierhttp://arxiv.org/abs/math/0101154
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98997
dc.subjectCategory Theory
dc.subject18A32; 18C15
dc.titleOn the monad of proper factorisation systems in categories
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