Related papers: Exactness and stability in homotopical algebra

In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…

In [math.AT/9907138] we proved that strongly homotopy algebras are homotopy invariant concepts in the category of chain complexes. Our arguments were based on the fact that strongly homotopy algebras are algebras over minimal cofibrant…

Consider a morphism between connected locally Noetherian normal schemes. In this paper, we discuss when the sequence of the etale fundamental groups associated to the morphism is exact. Moreover, we give a characterization of when the…

We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over…

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…

We define model structures on exact categories which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly…

Rump has recently showed the existence of a unique maximal Quillen exact structure on any additive category. We study when this is given by the stable short exact sequences, i.e. kernel-cokernel pairs consisting of a semi-stable kernel and…

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to…

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…

We study the stability of homological duality properties of Hopf algebras under extensions.

In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…

The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth…

In this monograph we develop various aspects of the homotopy theory of exact categories. We introduce different notions of compactness and generation in exact categories $E$, and use these to study model structures on categories of chain…

We introduce the notion of a "category with path objects", as a slight strengthening of Kenneth Brown's classic notion of a "category of fibrant objects". We develop the basic properties of such a category and its associated homotopy…

We study extensively the homotopy theory of coalgebras. By coalgebras, we mean the full theory of coalgebras: with counits and not necessarily locally conilpotent. For example $\mathcal E_\infty$-coalgebras, $\mathcal A_\infty$-coalgebras,…

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…

We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…

For A a category with finite colimits, we show that the embedding of A into the category of arrows Arr(A) determined by the initial object is the completion of A under strong homotopy cokernels. The nullhomotopy structure of Arr(A) (needed…