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Results tagged with limits-and-colimits
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user 294858
For questions on limits and colimts in the sense of category theory, and related notions.
4
votes
What does it mean for a category to be generated under (some) colimits?
It seems that dense generation does not imply 1-naïve generation in general. For a counterexample it is enough to consider the class $\Phi$ for small (or just finite) coproducts.
Indeed, given any non …
- 499
4
votes
Classification of absolute 2-limits?
A 2-category is Cauchy complete (in the sense you describe) if and only if idempotents splits, which is, if and only if its underlying ordinary category is Cauchy complete.
This holds more generally i …
- 499
6
votes
Accepted
Can every weighted colimit in a $\mathbf{Pos}$-enriched category be rephrased as a conical c...
Consider the terminal object $1\in\mathbf{Pos}$.
Then the closure of $1$ in $\mathbf{Pos}$ under all weighted colimits is $\mathbf{Pos}$ itself: If $X\in\mathbf{Pos}$, then $X\cong X\cdot 1$ is the co …
- 499