Pre-abelian Category - Examples

Examples

The original example of an additive category is the category Ab of abelian groups. Ab is preadditive because it is a closed monoidal category, the biproduct in Ab is the finite direct sum, the kernel is inclusion of the ordinary kernel from group theory and the cokernel is the quotient map onto the ordinary cokernel from group theory.

Other common examples:

  • The category of (left) modules over a ring R, in particular:
    • the category of vector spaces over a field K.
  • The category of (Hausdorff) abelian topological groups.

These will give you an idea of what to think of; for more examples, see abelian category (every abelian category is pre-abelian).

Read more about this topic:  Pre-abelian Category

Other articles related to "examples":

Proverbs in Advertising
... Tatira has given a number of examples of proverbs used in advertising in Zimbabwe ... However, unlike the examples given above in English, all of which are anti-proverbs, Tatira's examples are standard proverbs ... the English proverbs above are meant to make a potential customer smile, in one of the Zimbabwean examples "both the content of the proverb and the fact that it is phrased as a proverb ...
English Orthography - Spelling Irregularities - "Ough" Words
... though /oʊ/ as in toe (other examples dough) tough /ʌf/ as in cuff (other examples rough, enough) cough /ɒf/ as in off (other examples Gough (name, some pronunciations)) hiccough (a now ...

Famous quotes containing the word examples:

    It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.
    —G.C. (Georg Christoph)

    Histories are more full of examples of the fidelity of dogs than of friends.
    Alexander Pope (1688–1744)

    There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.
    Bernard Mandeville (1670–1733)