Questions tagged [internalization]

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What is the initial semiring category with a (commutative) semiring?

Recall that The biinitial monoidal category with a monoid is given by the augmented simplex category together with the monoid $([0],\sigma^{0}_{0},\delta^{0}_{0})$ there. The biinitial symmetric ...
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Reclusive Categories

Has there been any work done on internal categories inside internal categories? I'm familiar with $n$-fold categories, but I don't want an internal category inside the category of internal categories ...
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Internalizing 'topology on a set'

In any topos $\mathcal{S}$, we have the ability to speak about power objects $\mathcal{P}(X)$ of objects $X\in\mathcal{S}$. We can then define an internal closure operator as an arrow ${\sf cl}:\...
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