Related papers: Invariants additifs de dg-categories
It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
This is the second paper in a series on enumerative invariants counting self-dual objects in self-dual categories, and is a sequal to (arXiv:2302.00038). Ordinary enumerative invariants in abelian categories can be seen as invariants for…
This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of ``global conformal invariants''. Our theorem deals with such invariants P(g^n) that locally depend only on the…
We give a detailed account of the so-called "universal construction" that aims to extend invariants of closed manifolds, possibly with additional structure, to topological field theories and show that it amounts to a generalization of the…
We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is…
The commutative differential graded algebra $A_{\mathrm{PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal{I}}(X)$ of…
This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it…
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and $L_\infty$-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra…
This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…
We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting them. This gives a positive answer to a conjecture due to…
We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…
We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good…
The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let $\mathscr{X}$ denote an additive category with finite direct sums and split…
For a commutative quantale $\mathcal{V}$, the category $\mathcal{V}-cat$ can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor $T$ (formalised as an endofunctor on sets) can be…
We show an alternative construction of the cosimplicial free complete diferential graded Lie algebra $\mathfrak{L}_\bullet=\widehat{\mathbb{L}}(s^{-1}\Delta^\bullet)$ based on a new Lie bracket formulae for Lie polynomials on a general…
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…
We consider certain universal functors on symmetric quotient stacks of Abelian varieties. In dimension two, we discover a family of $\mathbb{P}$-functors which induce new derived autoequivalences of Hilbert schemes of points on Abelian…