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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 11th 2012

touched the formatting at additive category

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 18th 2016

I have added in the detailed proof of the proposition (here) that in an Ab-enriched category all finite (co-)products are biproducts.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 18th 2016

For completeness, further below in the Properties-section (starting here) I have spelled out the way semiadditive structure induces enrichment in commutative monoids, and that this induced enrichment coincides with the original enrichement if we started with an additive category.

These statements are scattered over other entries already, of course, but for readability if may be good to have them here in one place.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 7th 2016

I have expanded just a little more the (elementary) proof that in an Ab-enriched category finite products are biproducts (here). Maybe somewhat pedantically, but just to be completely clear.

• CommentRowNumber5.
• CommentAuthorTodd_Trimble
• CommentTimeJun 7th 2016

Note that subtraction is not needed: the result holds for $CMon$-enriched categories. In fact, having biproducts implies $CMon$-enrichment.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 7th 2016
• (edited Jun 7th 2016)

Yes, that’s discussed at biproduct. But since I am editing the entry on additive categories, I am talking there about Ab-enrichment.

[actually it’s also discussed further below in the entry on additive categories]

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJun 7th 2016

I have also made more explicit the (elementary) proofs of this prop. and this prop.