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Results tagged with limits-and-colimits
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user 2811
For questions on limits and colimts in the sense of category theory, and related notions.
7
votes
3
answers
644
views
Unexpected interaction between limits and colimits
Let $D$ be a limit-complete category. My vague question is: given two diagrams in $D$, what comparisons between them induce a morphism of their limits? I'm especially interested in the case that the c …
- 8,659
3
votes
Is the evaluation of polynomial functors appropriately continuous?
Ok, this follows trivially from the construction of limits in ${\bf Cat}$.
Let $I\ $ be a small category, let $X\colon I\to{\bf Cat}\ $ denote a functor, and let $Y=\text{colim}_{i\in I}X_i\ $ be it …
- 8,659
10
votes
1
answer
526
views
Is the evaluation of polynomial functors appropriately continuous?
I'd like a nice proof of the following fact.
Let $C$ and $D$ be categories, and let $\mathbf{Cat}/(C\times D)$ be the usual (1-categorical) slice category whose objects are triples $(X,F\colon X\to C …
- 8,659
6
votes
2
answers
220
views
Local finality condition (for re-indexing parameterized colimits)
I'm in need of a condition that is analogous to the "finality" condition in the following lemma:
Lemma: A functor $F\colon A\to B$ is final if and only if for any functor $x\colon B\to Set$, the natu …
- 8,659