Timeline for Weighted limits and Kan extension in Dist
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 3, 2023 at 9:13 | comment | added | varkor | Wood defines pointwise extensions in Abstract pro arrows I, as limits weighted by corepresentable distributors. If you look at the definition, it essentially coincides with the classical definition of pointwise right extension, e.g. here. | |
| May 3, 2023 at 8:37 | comment | added | nicolas | With the corrected definition of weighted limits I don't see how a pointwise kan extension is one.. I will post a new question | |
| May 3, 2023 at 6:57 | vote | accept | nicolas | ||
| May 3, 2023 at 6:28 | answer | added | varkor | timeline score: 2 | |
| May 3, 2023 at 5:32 | history | edited | nicolas | CC BY-SA 4.0 |
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| May 3, 2023 at 5:09 | history | edited | nicolas | CC BY-SA 4.0 |
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| May 2, 2023 at 15:01 | comment | added | nicolas | (any limit weighted by $P$ has the property that evaluating it at a specific functor $b:X\to B$ is the limit weighted by $\phi^b \otimes P$. we get the limit formula when we choose a functor from $X=1$, to which pointwise extension also evaluate to) | |
| May 2, 2023 at 14:57 | history | edited | nicolas | CC BY-SA 4.0 |
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| May 2, 2023 at 14:56 | comment | added | nicolas | as far as a I understand, a pointwise kan extension is a weighted limit (a specific one, weighted by $\phi_j$). what I am trying to understand is the difference between weighted limits and (representation of) Kan extension in $Dist$, the bicategory of distributors. | |
| May 2, 2023 at 14:53 | comment | added | varkor | A pointwise right extension along $j \colon A \to B$ in $\mathrm{Cat}$ is precisely a limit weighted by the corepresentable $B(1, j)$, hence a right extension along $B(1, j)$ in $\mathrm{Dist}$. Is this what you are asking? | |
| May 2, 2023 at 14:44 | history | edited | nicolas | CC BY-SA 4.0 |
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| May 2, 2023 at 14:38 | history | asked | nicolas | CC BY-SA 4.0 |