Related papers: A correspondence between proximity homomorphisms a…
To characterize categorical constraints - associativity, commutativity and monoidality - in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups…
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
We introduce bounded cohomology for (pairs of) groupoids and develop homological algebra to deal with it. We generalise results of Ivanov, Frigerio and Pagliantini to this setting and show that (under topological conditions) the bounded…
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We extend to one dimensional quotients the result of A. Conca and S. Murai on the convexity of the regularity of Koszul cycles. By providing a relation between the regularity of Koszul cycles and Koszul homologies we prove a sharp…
Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (\emph{coinduction functor}) which is right adjoint to the hom-functor represented by this comodule. Using the…
We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…
We study continuous bounded cohomology of totally disconnected locally compact groups with coefficients in a non-Archimedean valued field $K$. To capture the features of classical amenability that induce the vanishing of real bounded…
Pebble games are a powerful tool in the study of finite model theory, constraint satisfaction and database theory. Monads and comonads are basic notions of category theory which are widely used in semantics of computation and in modern…
A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$-theoretic regularity conditions, these…
We outline a definition of accessible and presentable objects in a 2-category $\mathcal K$ endowed with a "KZ context", that is to say a pair of lax-idempotent monads interacting in a prescribed way; this perspective suggests a unified…
An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying…
We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of $S^k \times S^l$, where $3 \le k < l \le 2k - 2$. The result is expressed in terms of Lie graph complex…
We study the geometry of the morphism between moduli spaces of hypersurfaces in $\mathbb P^{n-1}$ that sends a smooth hypersurface of degree $d+1$ to its associated hypersurface of degree $n(d-1)$. As a result, we obtain a compactification…
We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy…