Linear Extensions of Acyclic Categories

It is straightforward to generalize the classical notion of linear extension of posets, see Definition 2.20, to the context of acyclic categories. To underline this, we give here the definition using similar wording. 

It is easy to see, for example using induction, that an acyclic category has at least one linear extension. In a way, a converse of this statement is true as well if a category C has a linear extension and every morphism of an object into itself is an identity, then C must be acyclic. 

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