Search Results

Let $X$ be an arbitrary object in $\mathcal{C}$. I write $\{ W, F \}$ for the limit of $F$ weighted by $W$. By definition, $$\mathcal{C} (X, \{ W, F \}) \cong [\mathcal{I}, \textbf{Set}] (W, \mathcal{ …

This is going to be a long post, so let me state my question first and then explain what I am interested in by way of examples. Question. Is there any literature studying notions of generation under c …

Let $C$ be a small (1-)category. There is always a poset $D$ and a functor $p : D \to C$ such that: $p$ is surjective on objects, i.e. for every $c$ in $C$ there is a $d$ in $D$ such that $p (d) = c$ …

I assume $\varinjlim_{j : \mathcal{J}} \mathcal{I}_j = \mathcal{I}$ is meant in the strict sense of 1-categories. Since $\textbf{Cat}$ is cartesian closed, $$\textstyle [\mathcal{I}, \mathcal{C}] \con …

In enriched category theory, weighted limits may be strictly more general than conical limits, in the sense that an enriched category with all conical limits may fail to have all weighted limits. Howe …