category of sequences of abelian groups

This is the special case of the category of N\IN-graded modules over the N\IN-graded ring Z[T]\IZ[T] with deg⁡(T)=1\deg(T)=1. It can also be viewed as the category of functors from the category of natural numbers (N,≤)(\IN,\leq) to Ab\Ab. Thus, most (but not all) properties are inherited from Ab\Ab. A notable difference is that Ab(N,≤)\Ab^{(\IN,\leq)} is not one-sorted finitary algebraic.

Satisfied Properties

Assigned properties

—

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

—

Special objects

  • terminal object: the zero sequence 0→0→⋯0 \to 0 \to \cdots
  • initial object: the zero sequence 0→0→⋯0 \to 0 \to \cdots
  • products: degree-wise defined direct products
  • coproducts: degree-wise defined direct sums

Special morphisms

  • isomorphisms: morphisms that are bijective in each degree
  • monomorphisms: morphisms that are injective in each degree
  • epimorphisms: morphisms that are surjective in each degree
  • regular monomorphisms: same as monomorphisms
  • regular epimorphisms: same as epimorphisms

Indistinguishable categories

These categories in the database currently have exactly the same properties as the category of sequences of abelian groups. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.