Special Issue "Homological and Homotopical Algebra and Category Theory"
A special issue of Mathematics (ISSN 2227-7390).
Deadline for manuscript submissions: closed (31 March 2016).
Interests: K-theory; homotopical algebra; category theory; non-commutaive geometry
Interests: category theory; homological and homotopical algebra
Interests: categorical algebra; Galois theory; universal algebra
Interests: operads and their generalisations; Hochschild cohomology; enriched categories; higher categories; model categories
Interests: categorical algebra
The foundations of homological and homotopical algebra go back to the latter half of the previous century, to the works of S. Eilenberg, S. MacLane, and H. Cartan, and further to follow A. Dold and D. Quillen. Its aim is to study the properties of algebraic objects (groups, associative rings and algebras, Lie algebras, modules, monoids) using the methods of algebraic topology. It can also be viewed as a linearized version of homotopy theory of homotopy types. Nowadays, homological and homotopical algebra is a profound branch of mathematics, a fundamental and essential tool useful for many areas of mathematics, for example, class field theory, algebraic topology, and homotopy theory. That is illustrated by the famous Serre’s Conjecture, regarding the relationship between projective modules and free modules over polynomial rings. This problem of homological and commutative algebra, coming from algebraic geometry, was affirmatively proven in 1976. It has also helped to rewrite the foundations of algebraic geometry, to prove Weil Conjectures, and to create very powerful areas, such as homology theory of groups, Hochschild and cyclic homology theories, and algebraic K-theory. It should be noted that K-theory (algebraic and topological), based on fundamental works of A. Grothendieck, M. Atiyah, H. Bass, J. Milnor, and D.Quillen, is closely related to homotopical algebra and non-commutative geometry having applications to theoretical physics (string theory).
The beginnings of category theory go to A. Grothendieck and F.W. Lawvere in the 20th century. Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science. It is a general mathematical theory formalizing mathematical structures and their concept in terms of objects and arrows called morphisms. It is a powerful language, allowing us to see the universal components of a family of structures of a given kind, and how mathematical structures of different kinds are interrelated. It can be applied to mathematical logic and it is an alternative to set theory as a foundation of mathematics. Categorical methods are successfully used in homological algebra and algebraic topology.
Prof. Dr. Hvedri Inassaridze
Prof. Dr. Antonio Cegarra
Prof. Dr. Marino Gran
Prof. Dr. Michael Batanin
Prof. Dr. Zurab Janelidze
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed Open Access quarterly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. For this issue the Article Processing Charge (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections.
- Chain complexes and simplicial objects
- Commutative algebra
- Cohomology of groups
- Algebraic K-theory
- Homotopy theory
- Derived functors
- Homology theory of associative rings
- Spectral sequences
- Higher categories
- Cyclic homology
- Derived category
- Additive and homotopy functors
- Categorical algebra
- Projective dimension of rings