Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2307.06664 |
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Sommario:
- We investigate under which condition the $κ$-ind completion of a functor category $C^I$ is equivalent to the category of functors from $I$ to the $κ$-ind completion of $C$. A published theorem implies this is true for any Cauchy complete category $C$ and $κ$-small category $I$, but we show this is not the case in general. We prove two results that seem to cover all applications of this incorrect theorem we could find in the literature: The result holds if $C$ has $κ$-small colimits and $I$ is $κ$-small, or if $C$ is an arbitrary category and $I$ is well-founded and $κ$-small. In both cases, we show that the conditions are optimal in the sense that the result holds for all $C$ if and only if $I$ satisfies the given assumption.