67 citations · 146 across the 31 of their papers we have counts for
11 papers · 1 filter
On abelian 2-categories and derived 2-functors
Teimuraz Pirashvili
This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the mate…
Projective and injective objects in symmetric categorical groups
Teimuraz Pirashvili
We prove that the 2-category of symmetric categorical groups have enough projective and injective objects. This was conjectured by Bourn and Vitale in 2002 and was anounced recentl…
Categorical rings subsume ann-categories
Mamuka Jibladze, Teimuraz Pirashvili
The article has been withdrawn - the proof of the final corollary turned out to rely on an unproven statement. If the authors will manage to repair the argument, resubmission will…
Abelian categories versus abelian 2-categories
Teimuraz Pirashvili
Recently Dupont proved that the categories of discrete and codiscrete (or connected) objects in an abelian 2-category are equivalent abelian categories. He posses also a question w…
Universal coefficient theorem in triangulated categories
Teimuraz Pirashvili, Maria Julia Redondo
Let T be a triangulated category, A a graded abelian category and h: T -> A a homology theory on T with values in A. If the functor h reflects isomorphisms, is full and is such tha…
Quadratic algebra of square groups
H. -J. Baues, M. Jibladze, T. Pirashvili
There is a long-standing problem of algebra to extend the symmetric monoidal structure of abelian groups, given by the tensor product, to a non abelian setting. In this paper we sh…
Cohomology of the Grothendieck construction
Teimuraz Pirashvili, Maria Julia Redondo
We consider cohomology of small categories with coefficients in a natural system in the sense of Baues and Wirsching. For any funtor L: K -> CAT, we construct a spectral sequence a…
Comparison of Abelian categories recollements
Vincent Franjou, Teimuraz Pirashvili
We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.
Strengthening track theories
Hans-Joachim Baues, Mamuka Jibladze, Teimuraz Pirashvili
Using cohomology of categories with coefficients in natural systems it is proved that a groupoid enrichad category with pseudoproducts is pseudoequivalent to one with strict produc…
Linear extensions and nilpotence for Maltsev theories
Mamuka Jibladze, Teimuraz Pirashvili
Relationship is clarified between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of a…
On the PROP corresponding to bialgebras
Teimuraz Pirashvili
A PROP is a symmetric monoidal category, whose set of objects is the set of natural numbers and on objects the monoidal structure is given by the addition. An algebra over a PROP i…