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Results tagged with limits-and-colimits
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user 126667
For questions on limits and colimts in the sense of category theory, and related notions.
19
votes
Limits in category theory and analysis
In very special cases, the notions coincide. Let $R$ be the category (poset) whose objects are the real numbers and in which $Hom(x, y)$ has a single element if $x \leq y$ and is empty otherwise. Th …
- 25.2k
7
votes
Accepted
Commutation of limits and colimits: Is there a choice diagram?
This isn't true in general. Take $I = BG$ and $J = BH$ to be one-object groupoids, so that $A(i, j)$ becomes a set $A$ with commuting actions of $G$ and $H$. The left hand side is obtained by taking t …
- 25.2k
5
votes
Coend computation continued
The step $\int_{a \in A} \mathrm{Set}(\mathrm{hom}_A(a, a), S) = \mathrm{Nat}(\mathrm{hom}_A(-,-),S)$ does not really make sense, because $a \mapsto \mathrm{hom}_A(a,a)$ is not a functor. And $\int^{ …
- 25.2k