Talk:Preadditive category

Just for the record, I'll get to Additive_category and Pre-Abelian_category next week. — Toby Bartels, Friday, June 28, 2002

Please be more clear to non categorists

I came to this entry to see what is a preadditive category.

It is maybe correct and very clear to categorists and algebrists.

There is other kind of reader: the non expert. I have a general idea about categories, but I find the pages about categories too circular.

I think that the articles can be improved if more grounded examples are included. It is very confusing for the newcomer to read a category x is a category y combined with category z.

It is very common among categorists to assert that categories are very elegant and clearer, they however are not clear. One reason is the interest in showing the power of categories to express very dense concepts that not everybody knows. Other reason is that once they understand the concepts, they forget the effort to achieve it. Other is the lack of grounded examples, as mentioned above, the last I have in mind is that then not always use diagrams, or the ideas expressed in diagrams are not grounded.

In synthesis: please use pears and apples to show the concepts.

Algebroids

Using the definition of algebra over a commutative ring, why not include a link to R-algebroids and a note that an R-algebra is exactly an R-algebroid with one object? For example, k-Vect is a k-algebroid, for a field k, and similarly for k-Mod for a commutative ring k. We already know that a k-algebra is also equivalently a monoid in (k-Mod, ⊗, k). In this interpretation, a preadditive category is equivalently a 'ℤ-algebroid', or perhaps a 'ringoid'.