On the monad of proper factorisation systems in categories (*)
نویسنده
چکیده
It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the monad P = (–)2, in Cat. We show in this note that an analogous fact holds for proper (i.e., epimono) factorisation systems and a suitable quotient of the former monad, deriving from a construct introduced by P. Freyd for stable homotopy. Some similarities of P with the structure of the path endofunctor of topological spaces are considered. MSC: 18A32; 18C15.
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