CatGloss

Let $\mathbf{A}$ be a category and $X$ a presheaf on $\mathbf{A}$ . The category of elements $\mathbf{E}(X)$ of $X$ is the category in which: There is a projection functor $ P{\colon}\linebreak[0] \mathbf{E}(X) \to \mathbf{A} $ defined by $P(A, x) = A$ and $P(f) = f$ . The following `density theorem’ states that every presheaf is a colimit of representables in a canonical way.

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