Pre-abelian Category - Special Cases

Special Cases

  • An abelian category is a pre-abelian category such that every monomorphism and epimorphism is normal.

The pre-abelian categories most commonly studied are in fact abelian categories; for example, Ab is an abelian category.

Read more about this topic:  Pre-abelian Category

Other articles related to "special cases, case":

D'Alembert's Principle - Derivation For Special Cases
... This is true only for some very special cases e.g ... orthogonal to the constraint forces (which is not usually the case, so this derivation works only for special cases), the constraint forces do no work ...
Courts Of Chancery - Remedies
... Damages is money claimed in compensation for some failure by the other party to a case ... the Chancery Amendment Act 1858, which gave it that right, but in some special cases it had been able to provide damages for over 600 years ... In Cardinal Beaufort's case in 1453, for example, it is stated that "I shall have a subpoena against my feoffee and recover damages for the value of the land" ...
Semidiameter - Special Cases
... The semi-diameters of a non-circular ellipse are the halves of its extents along the two axes of symmetry ... They are the parameters a, b of the implicit equation Likewise, the semi-diameters of an ellipsoid are the parameters a, b, and c of its implicit equation The semi-diameters of a superellipse, superellipsoid, or superquadric can be identified in the same way ...
Circles - Computing Homothetic Centers - Special Cases
... If the circles have the same center but different radii, both the external and internal coincide with the common center of the circles ... This can be seen from the analytic formula, and is also the limit of the two homothetic centers as the centers of the two circles are varied until they coincide, holding the radii equal ...

Famous quotes containing the words cases and/or special:

    There are few cases in which mere popularity should be considered a proper test of merit; but the case of song-writing is, I think, one of the few.
    Edgar Allan Poe (1809–1845)

    The very best reason parents are so special . . . is because we are the holders of a priceless gift, a gift we received from countless generations we never knew, a gift that only we now possess and only we can give to our children. That unique gift, of course, is the gift of ourselves. Whatever we can do to give that gift, and to help others receive it, is worth the challenge of all our human endeavor.
    Fred Rogers (20th century)