Disjoint Union as a Coproduct

It is obvious that A commutes with coproducts, in other words, we have A C JD) = A C) ] A D). At the same time, it is important to note at this point that A does not commute with cohmits in general. The question of commutativity will be investigated in much more detail in Chapter 14. 

For future use, let n denote the poset with n elements and no order relations, i.e., n = iJT TT 

2 Stacks of Acyclic Categories and Joins of Regular TAisps 

Instead of putting two acyclic categories side by side, one can also put one on top of the other. 

Definition 10.7. LetC and D be two acyclic categories. The stack ofC and D is the acyclic category C 0 D defined by 

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