相关论文: Hochschild cohomology for functors on linear symme…

We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

We investigate Hochschild cohomology and homology of admissible subcategories of derived categories of coherent sheaves on smooth projective varieties. We show that the Hochschild cohomology of an admissible subcategory is isomorphic to the…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…

This paper expands further on a category theoretical formulation of Hochschild cohomology for monoid objects in monoidal categories enriched over abelian groups, which has been studied in arXiv:1605.00842. This topic was also presented at…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an…

We provide a factorization model for the continuous internal Hom, in the homotopy category of $k$-linear dg-categories, between dg-categories of equivariant factorizations. This motivates a notion, similar to that of Kuznetsov, which we…

Symmetric spectra were introduced by Jeff Smith as a symmetric monoidal category of spectra. In this paper, a detection functor is defined which detects stable equivalences of symmetric spectra. This detection functor is useful because the…

In this paper, we study the higher Hochschild functor and its relationship with factorization algebras and topological chiral homology. To this end, we emphasize that the higher Hochschild complex is a $(\infty,1)$-functor from the category…

Let $\mathcal C$ be category over a commutative ring $k$, its Hochschild-Mitchell homology and cohomology are denoted respectively $HH_*(\mathcal C)$ and $HH^*(\mathcal C).$ Let $G$ be a group acting on $\mathcal C$, and $\mathcal C[G]$ be…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it…

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of…

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

We compute endomorphisms of topological Hochschild homology ($\mathrm{THH}$) as a functor on stable $\infty$-categories, as well as variants thereof: we also compute endomorphisms of the $k$-linear Hochschild homology functor…

We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild…

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…

When studying deformations of an $A$-module $M$, Laudal and Yau showed that one can consider 1-cocycles in the Hochschild cohomology of $A$ with coefficients in the bi-module $End_k(M).$ With this in mind, the use of higher order Hochschild…