例句與造句

1. Then is an additive category, and equals the-fold power.
2. Almost all functors studied between additive categories are additive.
3. See pre-additive category for more.
4. Further facts about biproducts that are mainly useful in the context of additive categories may be found under that subject.
5. The original example of an additive category is the category of abelian groups "'Ab " '.
6. It's difficult to find additive category in a sentence. 用additive category造句挺難的
7. While these matrices are rather degenerate, they do need to be included to get an additive category, since an additive category must have a zero object.
8. While these matrices are rather degenerate, they do need to be included to get an additive category, since an additive category must have a zero object.
9. On the other hand, any equivalence between additive categories is necessarily additive . ( Note that the latter statement is not true for equivalences between preadditive categories .)
10. When considering functors between-linear additive categories, one usually restricts to-linear functors, so those functors giving an-module homomorphism on each hom-set.
11. Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms.
12. In fact, it is a theorem that all adjoint functors between additive categories must be additive functors ( see here ), and most interesting functors studied in all of category theory are adjoints.
13. As shown below, every semiadditive category has a natural addition, and so we can alternatively define an additive category to be a semiadditive category having the property that every morphism has an additive inverse.
14. This addition of morphism turns "'Ab "'into a preadditive category, and because the direct sum of finitely many abelian groups yields a biproduct, we indeed have an additive category.
15. Some authors have used the term " additive category " for preadditive categories, but here we follow the current trend of reserving this word for certain special preadditive categories ( see special cases below ).
16. Moreover, if both " C " and " D " are additive categories ( i . e . preadditive categories with all finite biproducts ), then any pair of adjoint functors between them are automatically additive.
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