On the monad of proper factorisation systems in categories

Details On the monad of proper factorisation systems in categories On the monad of proper factorisation systems in categories

2001-01-18

arxiv.org/abs/math/0101154v1

Mathematics

Category Theory

8 pages. Key Words: Factorisation systems, 2-monads, Eilenberg-Moore algebras, pseudo algebras

Scientific paper

It 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.

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