Related papers: Cohomology of Small Cartesian Closed Categories
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
We introduce a model structure on the category of graphs, which is Quillen equivalent to the category of $\mathbb{Z}_2$-spaces. A weak equivalence is a graph homomorphism which induces a $\mathbb{Z}_2$-homotopy equivalence between their box…
The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…
The (co)homology self-closeness number of a simply-connected based CW-complexes $X$ is the minimal number $k$ such that any self-map $f$ of $X$ inducing an automorphism of the (co)homology groups for dimensions$\leq k$ is a self-homotopy…
In this note we prove an equivariant version of a result of Cartan for equivariant simplicial cohomology with local coefficients.
We review Haefliger's differentiable cohomology for the pseudogroup of diffeomorphisms of $\mathbb{R}^q$. We investigate the structure needed to define such a cohomology, which, remarkably, is related to the so called Cartan distribution…
We use derived methods to study the Gauss-Manin connection in Hochschild homology, infinitesimal cohomology, and derived de Rham cohomology. As applications, we give new approaches to nilinvariance, the Quillen spectral sequence, and the…
We prove Rietsch's mirror conjecture that the Dubrovin quantum connection for minuscule flag varieties is isomorphic to the character D-module of the Berenstein-Kazhdan geometric crystal. The idea is to recognize the quantum connection as…
Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…
In this article we build a Quillen model category structure on the category of sequentially complete l.m.c.-C*-algebras such that the corresponding homotopy classes of maps Ho(A,B) for separable C*-algebras A and B coincide with the…
We establish a general method to produce cofibrant approximations in the model category $U_S(C,D)$ of $S$-valued $C$-indexed diagrams with $D$-weak equivalences and $D$-fibrations. We also present explicit examples of such approximations.…
We compute the small cohomology ring of the Cayley Grassmannian, that parametrizes four-dimensional subalgebras of the complexified octonions. We show that all the Gromov-Witten invariants in the multiplication table of the Schubert classes…
We develop a theory of Cech-Bott-Chern cohomology and in this context we naturally come up with the relative Bott-Chern cohomology. In fact Bott-Chern cohomology has two relatives and they all arise from a single complex. Thus we study…
We introduce a cohomology theory for spatial super- product systems and compute the $2-$cocycles for some basic examples called as Clifford super-product systems, thereby distinguish them up to isomorphism. This consequently proves that a…
We generalize some of the fundamental results of algebraic topology from topological spaces to \v{C}ech's closure spaces, also known as pretopological spaces. Using simplicial sets and cubical sets with connections, we define three distinct…
In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the…
In this note, we survey our recent work concerning cohomologies of harmonic bundles on quasi-compact Kaehler manifolds.
We establish a Dwyer-Kan equivalence of relative categories of combinatorial model categories, presentable quasicategories, and other models for locally presentable (infinity,1)-categories. This implies that the underlying quasicategories…
In this paper we study a new notion of category weight of homology classes developing further the ideas of E. Fadell and S. Husseini. In the case of closed smooth manifolds the homological category weight is equivalent to the cohomological…
Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the…