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1. • CommentRowNumber1.
   • CommentAuthorPaoloPerrone
   • CommentTimeJun 21st 2021
   • (edited Jun 21st 2021)
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   Author: PaoloPerrone
   Format: MarkdownItexWhat are examples of [[rig categories]] which - are not just rigs or ordered rigs, and - are not distributive monoidal categories (so the sum is not the coproduct)? I cannot seem to come up with an example myself except very artificial ones (such as taking a distributive monoidal category and removing some arrows). I'm sure there's quite some though, can anyone help?

   What are examples of rig categories which

   • are not just rigs or ordered rigs, and
   • are not distributive monoidal categories (so the sum is not the coproduct)?

   I cannot seem to come up with an example myself except very artificial ones (such as taking a distributive monoidal category and removing some arrows). I’m sure there’s quite some though, can anyone help?

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 21st 2021
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   Author: Todd_Trimble
   Format: MarkdownItexIt's a good question. Does it work to take a symmetric monoidal category and look at strong symmetric monoidal endofunctors on that?

   It’s a good question. Does it work to take a symmetric monoidal category and look at strong symmetric monoidal endofunctors on that?

3. • CommentRowNumber3.
   • CommentAuthorPaoloPerrone
   • CommentTimeJun 21st 2021
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   Author: PaoloPerrone
   Format: MarkdownItexThat seems to work. Nice example!

   That seems to work. Nice example!