Timeline for Are there categories whose internal hom is somewhat 'exotic'?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2019 at 9:03 | comment | added | Qiaochu Yuan | I like your subtraction example! It generalizes to any group, regarded as a discrete monoidal category. | |
| Aug 19, 2019 at 19:13 | comment | added | seldon | *obviously I meant to write $y \to z = \neg y \lor z$. | |
| Aug 18, 2019 at 21:38 | comment | added | seldon | Just to add to your last example: to see why the internal hom is $z-y$, it is a fact of life that in an Heyting algebra (aka postal Cartesian closed small category), $y \to z = \neg y \lor y$, where the 'negation' of $y$ is $y \to 0$ (this also solves the exercise about complements in power sets). Therefore if we unpack the universal property defining $\to$ we get $x+y \leq 0 \iff x \leq y \to 0$, so $\neg y = y \to 0 = - y$ as expected. | |
| Aug 18, 2019 at 21:31 | history | edited | Tom Leinster | CC BY-SA 4.0 |
deleted 6 characters in body
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| Aug 18, 2019 at 21:29 | comment | added | seldon | Yes! Heyting algebras are what I was looking at when I thought my question. So I was waiting for this answer (I would have written it myself tomorrow). Still, yours is surely better than what I would have written, in particular the last example I really cool. | |
| Aug 18, 2019 at 21:15 | history | answered | Tom Leinster | CC BY-SA 4.0 |