Geodesic
A Note on Exact Colimits
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 569-572

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This note proves another special case of a conjecture of U. Oberst. Oberst considered [1], for any small category , the X abelian category of abelian group-valued functors on , and the X functor Colim: which takes each diagram to its colimit. The question is, when is Colim exact? For its relationships, see [1], It is a sufficient condition that each component of is upward filtered. Oberst conjectured that it is also necessary, and proved this under some conditions. He mentioned particularly the case that is a monoid, i.e. a category with one object. We shall verify the conjecture in that case. 
Isbell, John R. A Note on Exact Colimits. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 569-572. doi: 10.4153/CMB-1968-068-7
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     title = {A {Note} on {Exact} {Colimits}},
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