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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

3 votes
1 answer
512 views

Examples of functors $\mathbf{Set} \to \mathbf{Set}$ which are not analytic

Let $\mathbb{B}$ denote the groupoid of finite sets and bijections. A functor $F : \mathbf{Set} \to \mathbf{Set}$ is analytic if it is the left Kan extension of some functor $G : \mathbb{B} \to \math …
7 votes
1 answer
339 views

Generalizing indexed coproduct from $\mathrm{Set}$ to other monoidal categories

Consider the diagonal functor $\Delta_\mathcal{J} : \mathrm{Set} \to \mathrm{Set}^\mathcal{J}$, given by $\Delta_{\mathcal{J}}(X) = J \mapsto X$. This has left and right adjoints, which in the case t …