Related papers: Higher colimits, derived functors and homology
We adopt the viewpoint that topological And\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on…
We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…
We define Anderson-Brown-Cisinski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibration categories. Homotopy colimits for Quillen model categories are obtained as a particular case. We…
In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to…
As an instance of a linear action of a Hopf algebra on a free associative algebra, we consider finite group gradings of a free algebra induced by gradings on the space spanned by the free generators. The homogeneous component corresponding…
Colimits are a fundamental construction in category theory. They provide a way to construct new objects by gluing together existing objects that are related in some way. We introduce a complementary notion of anticolimits, which provide a…
We introduce acyclic polygraphs, a notion of complete categorical cellular model for (small) categories, containing generators, relations and higher-dimensional globular syzygies. We give a rewriting method to construct explicit acyclic…
We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…
The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory that algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes…
We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…
Recently, important progress has been made in the study of finite-dimensional semisimple Hopf algebras over a field of characteristic zero. Yet, very little is known over a field of positive characteristic. In this paper we prove some…
We study the higher derived functors of the inverse limit of a functor F: D --> Z_{(p)}-mod, where D is one of the standard categories which arise when studying the homotopy theory of the classifying space of a finite group G, e.g., the…
We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we…
We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg: If a finite dimensional self-injective algebra has a module of complexity at least…
We show that the higher-order Weyl algebras over a field of characteristic zero, which are formally rigid as associative algebras, can be formally deformed in a nontrivial way as hom-associative algebras. We also show that these…
We present a detailed computation of the cyclic and the Hochschild homology and cohomology of generic and 3-Calabi-Yau homogeneous down-up algebras. This family was defined by Benkart and Roby in their study of differential posets. Our…
It is becoming increasingly difficult for geometers and even physicists to avoid papers containing phrases like `triangulated category', not to mention derived functors. I will give some motivation for such things from algebraic geometry,…
The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…
Making use of the recent theory of noncommutative motives, we prove that every additive invariant satisfies Galois descent. Examples include mixed complexes, Hochschild homology, cyclic homology, periodic cyclic homology, negative cyclic…
We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen…