Related papers: The Lusternik-Schnirelmann category for a differen…
We describe a bicategory $(\mathcal{R}ed\,\mathcal{O}rb)$ of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using…
We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…
A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds…
Distributive Stonean residuated lattices are closely related to Stone algebras since their bounded lattice reduct is a Stone algebra. In the present work we follow the ideas presented by Chen and Gr\"{a}tzer and try to apply them for the…
In this paper we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules…
A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…
In a previous work, we have associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we have also a realization functor from the category of complete differential graded Lie…
We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense for any constructible sheaf theory (such as l-adic sheaves).…
We define the notion of fundamental group of an algebraic stack, prove a comparison theorem between the fundamental group of a stack over the complex numbers and that of the associated analytic orbifold, show that this notion coincides with…
We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…
We show that the category of vector fields on a geometric stack has the structure of a Lie 2-algebra. This proves a conjecture of R.~Hepworth. The construction uses a Lie groupoid that presents the geometric stack. We show that the category…
We prove a Dold-Kan type correspondence between the category of dendroidal abelian groups and a suitably constructed category of dendroidal complexes. Our result naturally extends the classical Dold-Kan correspondence between the category…
In this note, we completely classify left-invariant Riemann solitons on three-dimensional Lorentzian Lie groups.
Extending a result of F\'elix-Halperin-Lemaire on Lusternik-Schnirelmann category of products, we prove additivity of a rational approximation for Schwarz's sectional category with respect to products of fibrations.
Let A denote the ring of differential operators on the affine line with its two usual generators t and d/dt given degrees +1 and -1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups…
We classify Lie n-algebras possessing an invariant lorentzian inner product.
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial for the…
Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical…
We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labeled by an arbitrary finite-dimensional representation.…