Semi-abelian categories

By George Janelidze, L. Márki, Walter Tholen. 2002

537 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a1a57a21594b46a2a6ed4d0e3322b5539704efaf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Marino Gran
2. Tim Van der Linden
3. Sandra Mantovani
4. Giuseppe Metere
5. Dominique Bourn
6. Maria Manuel Clementino
7. Walter Tholen
8. Dikran Dikranjan

In Artificial Intelligence

1. Marino Gran
2. Tim Van der Linden
3. Dominique Bourn
4. Walter Tholen
5. Dikran Dikranjan

In Mathematical Physics

1. Marino Gran
2. Tim Van der Linden
3. Dominique Bourn
4. Walter Tholen
5. Sandra Mantovani
6. Giuseppe Metere
7. Maria Manuel Clementino
8. Dikran Dikranjan

Citations in the corpus

• Normalities and commutators (2010, background): “l. through k. f,f′ regular epis. +3 +3 +3 +3 Mal’cev ks Regular ks Mal’cev + Regular ks 6 3. Semi-abelian, homological and ideal-determined categories. Semi-abelian categories have been introduced in [JMT02] in order to recapture algebraic properties of groups, rings etc. in a categorical-theoretica”
• On the second cohomology group in semi-abelian categories (2005, methodology): “The second one is the notion of central arrows, first defined by Huq [28] in a context that is essentially equivalent to the context of semi-abelian categories [31].”
• Baer invariants in semi-abelian categories I:General theory (2004, unknown): “This notion was introduced by Janelidze, Márki and Tholen in [28].”
• On the representability of actionsin a semi-abelian category (2005, unknown): “So ET is already semi-abelian by [25] 2.”
• Centrality and connectors in Maltsev categories (2002, background): “Any protomodular category [2] is Maltsev, and then i np articular any semiabelian, and any abelian category [ 19 ].”
• Characterization of protomodular varieties of universal algebras (2003, unknown): “Protomodular categories were first introduced in [2]; their role in algebra, and various further developments are also described in [3]-[ 6 ].”
• Topological semi-abelian algebras (2005, background): “A semi-abelian category V is finitely cocomplete (see [20]), admits semi-direct products (see [12]), satisfies the five lemma, the nine lemma, the snake lemma (see [10]), the Noether isomorphism theorems (see [5]) and the Jordan–Hölder theorem (see [6]).”
• Baer invariants in semi-abelian categories II: Homology (2004, unknown): “This means that A is pointed, Barr exact and Bourn protomodular with binary coproducts [25].”