If \\( D : \textbf{1} \rightarrow \textbf{Set} \\) is a functor, what is the limit of \\(D\\)?
Compute it using [**Theorem 3.90**](https://forum.azimuthproject.org/discussion/2165),
and check your answer against **Definition 3.87**.

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**Definition 3.87**

Let \\( D : \mathcal{J} \rightarrow \mathcal{C} \\) be a diagram.
A _cone_ \\( (C, c_* ) \\) over \\(D\\) consists of

(i) an object \\( C \in Ob(\mathcal{C} \\);

(ii) for each object \\( j \in Ob(\mathcal{J}) \\), a morphism \\( c_j : C \rightarrow D(j) \\).

To be a cone, these must satisfy the following property:

(a) for each \\( f : i \rightarrow j \\) in \\( \mathcal{J} \\) , we have \\( c_j = c_i . D( f ) \\).

A morphism of cones \\( (C, c_* ) \rightarrow (C' , c'_* ) \\)
is a morphism \\( a : C \rightarrow C' \\) in \\( \mathcal{C} \\) such that for
all \\( j \in \mathcal{J} \\) we have \\( c_j = a.c'_j \\).
Cones over \\(D\\), and their morphisms, form a category \\( \textbf{Cone}(D) \\).

The _limit_ of \\(D\\), denoted \\( lim(D) \\), is the terminal object in the category \\( \textbf{Cone}(D) \\).
Say it is the cone \\( lim(D) = (C, c_* ) \\); we refer to \\(C\\) as the _limit object_ and
the map \\(c_j\\) for any \\( j \in \mathcal{J} \\) as the \\(j^{th}\\) _projection map_.