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Mamuka Jibladze

Publications and source records attributed to Mamuka Jibladze.

23 records · Page 2Linked to original sources
arXiv2004

Secondary derived functors and the Adams spectral sequence

Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can be performed. We introduce secondary chain complexes and secondary resolutions leading to the concept of secondary derived functors. As a main result we show that the E_3-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E_3-term explicitly by an algorithm.

math.AT↗
arXiv2004

Computation of the E_3-term of the Adams spectral sequence

An algorithm is described giving effective determination of the second differential in the Adams spectral sequence. The algorithm is based on the notion of secondary derived functor, and on the explicit algebraic model of the groupoid enriched category of stable maps and stable tracks between Eilenberg-Mac Lane spaces.

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arXiv2003

Strengthening track theories

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 products.

math.CT↗
arXiv2002

Linear extensions and nilpotence for Maltsev theories

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 algebras turn out to be nilpotent Maltsev precisely when their theories may be obtained as results of iterated linear extensions by bifunctors from the so called abelian theories. The latter theories are described; they are slightly more general than theories of modules over a ring.

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