19 июл. 2024 г. · An Ab Ab -enriched category (or, if small, ringoid) is a category enriched over the monoidal category Ab of abelian groups with its usual tensor ...

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal ... Examples of enriched categories · Enriched functors

9 дек. 2023 г. · In particular, taking K to be ℤ (the ring of integers), a ringoid (or Ab-enriched category) is a category enriched over Ab. A (Lawvere) metric ... Enrichment in a monoidal... · Passage between ordinary...

28 июн. 2021 г. · A one object Ab-enriched category is exactly a ring. The category corresponds to the monoid (multiplication) of the ring and the Ab-enrichment to the addition ... What are abelian categories enriched over themselves? Can a category be enriched over abelian groups in more than ... Examples of enriched categories which are (co)powered or (co ... Is there a sensible way to enrich over SymMonCat such that ... Другие результаты с сайта mathoverflow.net

2 мая 2024 г. · A preadditive category is another name for an Ab-category, ie, a category that is enriched over the category of abelian groups, Ab. I've read that abelian categories can naturally be enriched in enriched categories are - k - -modules of - Math Stack Exchange If we have finite coproducts in Ab-enriched category, does it ... Definition of a Functor of Abelian Categories Другие результаты с сайта math.stackexchange.com

16 мая 2018 г. · Ab is the Ab-enriched category in which, for abelian groups <A, 0, +, -> and <B, 0, +, ->, the group structure on the set of group homomorphisms ...

Since Ab-categories are additionally equipped with the structure of abelian groups on their Hom-sets, it's natural that we ask that functors between Ab- ...

In mathematics, specifically in category theory, a preadditive category is another name for an Ab-category, ie, a category that is enriched over the category ... Additive functors · R-linear categories · Biproducts

An Ab-category is additive when its underlying category has a terminal object and finite products; By the yoga above, this implies that the terminal object is ...

Well-known examples of such categories are CommMon, the category of commutative monoids, Ab, the category of abelian groups (both having all finite biproducts - ...