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1. • CommentRowNumber1.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 26th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexHappened to notice a question at [[bicartesian closed category]]. > Question: don't you need *distributive* bicartesian closed categories to interpret intuitionistic propositional logic? Consider the or-elimination rule > $$ \frac{\Gamma, A \vdash C \qquad \Gamma,B \vdash C} {\Gamma, A + B \vdash C} $$ > The intepretations of the two premises will be maps of type $\Gamma \times A \to C$ and $\Gamma \times B \to C$. Then the universal property of coproducts gets us to $(\Gamma \times A) + (\Gamma \times B) \to C$, but we can't get any farther -- we need a distributivity law to get $\Gamma \times (A+B) \to C$.

   Happened to notice a question at bicartesian closed category.

   Question: don’t you need distributive bicartesian closed categories to interpret intuitionistic propositional logic? Consider the or-elimination rule

   $$\frac{\Gamma, A \vdash C \qquad \Gamma,B \vdash C} {\Gamma, A + B \vdash C}$$

   The intepretations of the two premises will be maps of type $\Gamma \times A \to C$ and $\Gamma \times B \to C$. Then the universal property of coproducts gets us to $(\Gamma \times A) + (\Gamma \times B) \to C$, but we can’t get any farther – we need a distributivity law to get $\Gamma \times (A+B) \to C$.

2. • CommentRowNumber2.
   • CommentAuthorUlrik
   • CommentTimeJul 26th 2011
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   Author: Ulrik
   Format: MarkdownItexI've added a short paragraph to address this. Does this need a more thorough answer? If not, should I remove the question block?

   I’ve added a short paragraph to address this.

   Does this need a more thorough answer?

   If not, should I remove the question block?

3. • CommentRowNumber3.
   • CommentAuthorUlrik
   • CommentTimeJul 27th 2011
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   Author: Ulrik
   Format: MarkdownItexThe anonymous questioner acknowledged that the edit was to satisfactory, so I removed the question block.

   The anonymous questioner acknowledged that the edit was to satisfactory, so I removed the question block.

4. • CommentRowNumber4.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 27th 2011
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   Author: Andrew Stacey
   Format: MarkdownItexIncidentally, when replying to questions like this that are written directly on the nLab, it's probably worth (briefly) pointing out that they'd get a better chance of an answer if they posted it at the nForum (which can be done anonymously). I only happened across this question by chance.

   Incidentally, when replying to questions like this that are written directly on the nLab, it’s probably worth (briefly) pointing out that they’d get a better chance of an answer if they posted it at the nForum (which can be done anonymously). I only happened across this question by chance.

5. • CommentRowNumber5.
   • CommentAuthorNeel Krishnaswami
   • CommentTimeJul 27th 2011
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   Author: Neel Krishnaswami
   Format: MarkdownItexHi Andrew and Ulrik: I asked that question. It didn't occur to me to ask it here, since the average level of discussion is quite a bit more sophisticated than my rather elementary question. If you think it won't bring down the tone, I'm happy to ask similar questions here in the future. :)

   Hi Andrew and Ulrik:

   I asked that question. It didn’t occur to me to ask it here, since the average level of discussion is quite a bit more sophisticated than my rather elementary question. If you think it won’t bring down the tone, I’m happy to ask similar questions here in the future. :)

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 27th 2011
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   Author: Todd_Trimble
   Format: MarkdownItexNeel, please feel free to ask any questions at any level. There are plenty of elementary questions that get asked here.

   Neel, please feel free to ask any questions at any level. There are plenty of elementary questions that get asked here.

7. • CommentRowNumber7.
   • CommentAuthorAndrew Stacey
   • CommentTimeJul 27th 2011
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   Author: Andrew Stacey
   Format: MarkdownItex<http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=2932> being a case in point!

   http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=2932 being a case in point!