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# Category = GrupooidGroupoid x Poset?

Is it possible to split a given category $C$ up into its grupoid groupoid of isomorphisms and a category that resembles a poset?

"Splitting up" should be that $C$ can be expressed as some kind of extension of a grupoid groupoid $G$ by a poset $P$ (or "directed category" $P$ the only epimorphisms in $P$ are the identities, all isomorphisms in $P$ are identities).

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# Category = Grupooid x Poset?

Is it possible to split a given category $C$ up into its grupoid of isomorphisms and a category that resembles a poset?

"Splitting up" should be that $C$ can be expressed as some kind of extension of a grupoid $G$ by a poset $P$ (or "directed category" $P$ the only epimorphisms in $P$ are the identities, all isomorphisms in $P$ are identities).