3 x 3 lemma for star-exact sequences
Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
INT PRESS BOSTON, INC
Abstract
ENGLISH ABSTRACT: A regular category is said to be normal when it is pointed
and every regular epimorphism in it is a normal epimorphism. Any abelian category is normal, and in
a normal category one can define short exact sequences in a similar way as in an abelian category.
Then, the corresponding 3 × 3 lemma is equiv- alent to the so-called subtractivity, which in
universal algebra is also known as congruence 0-permutability. In the context of non-pointed
regular categories, short exact sequences can be replaced with “exact forks” and then, the
corresponding 3 × 3 lemma is equivalent, in the universal algebraic terminology, to congruence
3-permutability; equivalently, regular categories sat- isfying such 3 × 3 lemma are precisely the
Goursat categories. We show how these two seemingly independent results can be unified in the
context of star-regular categories recently intro- duced in a joint work of A. Ursini and the first
two authors.
Description
CITATION: Gran, M., Janelidze, Z & Rodelo, D. 2012. 3 X 3 lemma for star-exact sequences. Homology Homotopy Appl. 14 (2) 1 - 22, 2012.
The original publication is available at https://projecteuclid.org/
The original publication is available at https://projecteuclid.org/
Keywords
Citation
Gran, M., Janelidze, Z & Rodelo, D. 2012. 3 X 3 lemma for star-exact sequences. Homology Homotopy Appl. 14 (2) 1 - 22, 2012.