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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.
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
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 …
- 30.3k
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