Mobius function for acyclic categories

The Mobius function for posets is in fact a special case of the notion of a Mobius function for acyclic categories. 

Definition 10.25. Let C he an acyclic category with a terminal object t. A function jj, 0 C) h is defined as follows  

For future reference, we mention that moving all summands in (10.19) over to the left-hand side, we get 

In analogy with Hall s theorem we have the following statement. 

Theorem 10.26. For any finite acyclic category C with an initial object s and a terminal object t, we have 

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Fig. 10.19. Mobius functions for acyclic categories from Figure 10.1 with added...

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