Related papers: A sufficient criterion for homotopy cartesianess

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category. Given a composition of two commutative squares in $\mathcal{C}$, if two commutative squares are homotopy cartesian, then their composition is also a homotopy…

We prove that the homotopy type of a map from a Peano continuum into a planar or one-dimensional space is determined by the induced homomorphism of fundamental groups. This provides a new proof that planar sets are aspherical and is used to…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

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…

A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…

We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy…

We prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of…

We establish certain conditions which imply that a map $f:X\to Y$ of topological spaces is null homotopic when the induced integral cohomology homomorphism is trivial; one of them is: $H^*(X)$ and $\pi_*(Y)$ have no torsion and $H^*(Y)$ is…

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

We call a diagram D absolutely cartesian if F(D) is homotopy cartesian for all homotopy functors F. This is a sensible notion for diagrams in categories C where Goodwillie's calculus of functors may be set up for functors with domain C. We…

A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y) provided the ambient model category is right proper and…

In a triangulated category, cofibre fill-ins always exist. Neeman showed that there is always at least one "good" fill-in, i.e., one whose mapping cone is exact. Verdier constructed a fill-in of a particular form in his proof of the $4…

We define a homomorphism from (a certain extension of) the fundamental group of the Hamiltonian automorphism group of a symplectic manifold to the group of invertibles in its quantum cohomology ring. The manifold must satify a technical…

We propose the notion of partial resolution of a ring, which is by definition the endomorphism ring of a certain generator of the given ring. We prove that the singularity category of the partial resolution is a quotient of the singularity…

A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Kaplansky implies that any simple compact ring is finite. We…

Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…

Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of…