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Results tagged with slice-categories
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user 152679
7
votes
Dependent sum/product and the base-change functor adjunctions
Categorically, the right adjoint $\Pi_f$ exists when $f$ is exponentiable. In the categorical semantics of type theory, exponentiable maps correspond to the display maps. There are several ways one ca …
- 10.7k
13
votes
Accepted
Overloading of the word "local" in category theory
The terminology situation is certainly unfortunate. There is an nLab page for locally, which lists the different usages of the term (it doesn't currently include those for "local" rather than "locally …
- 10.7k
2
votes
0
answers
92
views
Coslices of $\mathbb D$-presentable categories
Let $\mathbb D$ be a sound limit doctrine. When $\mathbb D$ is the doctrine of $\lambda$-small limits, then for any $\mathbb D$-presentable category $\mathscr C$ and $X \in \mathscr C$, the coslice $X …
- 10.7k