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Definition 4.22.2. Let $\mathcal{C}$ be a category. A directed system $(M_ i, f_{ii'})$ is an essentially constant system if $M$ viewed as a functor $I \to \mathcal{C}$ defines an essentially constant diagram. A directed inverse system $(M_ i, f_{ii'})$ is an essentially constant inverse system if $M$ viewed as a functor $I^{opp} \to \mathcal{C}$ defines an essentially constant inverse diagram.

Comments (2)

Comment #6722 by Alejandro González Nevado on

Shouldn't both appearences of be substitute by as we see functors going between categories and is the category associated to the set , which are not exactly the same thing? If this is not the case I apologize but then I did not see before in the text the definition of for a preordered set (although it is obviously a clear thing).

Comment #6917 by on

The relationship between systems over and diagrams whose index category is the category associated to is discussed in Section 4.21. I think the definition as stated here is sufficiently clear, although of course a machine wouldn't be able to read it. One way to change the definition would be to remove the equation and just say " viewed as a functor". I don't think that would be so helpful.

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  • 9 comment(s) on Section 4.22: Essentially constant systems

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