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The General Construction and Further Examples

The construction from the previous subsection can put into a more general context, which, gratifyingly, will then specialize to further useful and interesting notions. [Pg.75]

There are several special cases of the comma category construction. First, taking A = 1, B = C, G = id , and taking F 1 — G to be the functor mapping the unique object of 1 to some given object x G 0 C) gives the category [x [ C) described in Definition 4.35. [Pg.75]

Another example is provided when we take A = B = C and F = G = idc-This gives the category of all morphisms of G, often called the category of arrows of G, with the new morphisms being all commuting diagrams of old morphisms. [Pg.75]

Finally, let us remark that it is possible to take one of the functors F and G in Definition 4.36 contravariant. This will also yield a category, which we denote by 0(F°p G) if F is taken to be contravariant, and 0 F J. G°p) if G is taken to be contravariant. This construction will come in handy when we define the analogue of intervals for acyclic categories. [Pg.75]


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