Limit Constructions

If we have a functor. F Ci — C2 and a G-action on a 0 Ci), then by composing T with the functor encoding the group action, we get a functor from G to C2. This is the so-called induced action. 

For example, an action on an abstract simplicial complex induces an action on the underlying topological space this is a composition with the geometric realization functor. An action on a poset P induces an action on the order complex A P), which is defined in Chapter 9 this is a composition with the order complex functor. Furthermore, it induces a G-action on any given homology group Hi A P)] TZ), which, in case 7 . is a field, is the same as a linear representation of G over TZ. 

Colimit is a very useful notion in all sorts of combinatorial contexts. We shall give a hands-on definition and refer the reader to standard texts [McL98, Mit65] for further details. 

Let Cl and C2 be two categories and let F Ci — C2 be a functor between them. Intuitively, one can think of this functor as a diagram, a picture in which some objects of C2 are connected with arrows. These objects are the images of objects of Cl under F, and the arrows are the images of morphisms of Ci under F. Accordingly, the arrows should compose right, as is prescribed by functor axioms. 

Let us call a sink of F an object L of C2, together with a collection of morphisms pointing from the objects in the diagram to the object L, i.e., F a) L, for all a e G(Gi), such that these new morphisms commute appropriately with the old morphisms in the diagram. Formally, we require that for all m A4ci (oij 02) we have o F(rn) =.  

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Operate below minimum oxygen concentration Practice good housekeeping Grind/blend under inert atmosphere Provide damage limiting construction... 

Damage Limiting Construction Construction of equipment (building) with weak sections to limit the damage to the equipment (building). The weak sections fail early and prevent damage to the rest of the equipment (building). 

Designation No. Significant Feature Applications Best Suited Limitations Construction... 

In the fully industrialized countries, there is only limited construction of new factories, power generation plants, or large hospitals, office towers, and the like. Consequently there is an equally limited number of entirely new cooling systems. Moreover, such existing cooling systems as are currently in operation are, for the most part, already being provided with water treatment programs. 

Thailand is primarily an agrarian economy as evidenced in Table 9.20. The major fertilizer company was considering a large expansion using locally produced ammonia as feedstock. If this occurred, the domestic natural gas supply would have to be apportioned, or imports would be needed, to supply the petrochemical projects. In early 1999 there were 18 projects on hold or under limited construction until the economic situation eases [13]. 

Figure 6-12 depicts various building layouts incorporating spatial separation and damage limiting construction. 

Factory Mutual Engineering Corporation, Damage-Limiting Construction. Loss Prevention Data Sheet 1-44, Norwood, MA, July, 1991. 

Reduction of moisture load Limit construction moisture Initially dry materials... 

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