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),

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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_.