Related papers: Homological kernels of monoidal functors

If X is a CW complex, one can assign to each point of X an ordered abelian group of finite rank whose subset of positive elements depends continuously on the points of X. A locally trivial bundle which arises in this way we denote by E(X).…

We systematically develop the theory of definable functors between compactly generated triangulated categories. Such functors preserve pure triangles, pure injective objects, and definable subcategories, and as such appear in a wide range…

Cohomology theories with values in LCA (locally compact abelian) groups suffer from the problem that the latter do not form an abelian category. However, the category LCA has a canonical abelian category envelope, the heart of a suitable…

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

We study abelian envelopes for pseudo-tensor categories with the property that every object in the envelope is a quotient of an object in the pseudo-tensor category. We establish an intrinsic criterion on pseudo-tensor categories for the…

A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…

In this paper we define the tensor product of two A$_{\infty}$-categories and two A$_{\infty}$-functors. This tensor product makes the category of A$_{\infty}$-categories symmetric monoidal (up to homotopy), and the category…

The aim of this paper is to introduce a tensor structure for the Serre quotient category of an abelian monoidal category with biexact tensor product to make the canonical functor a monoidal functor. In this tensor product, the Serre…

We show how monoidal adjunctions can be used to prove the existence of monoidal abelian envelopes of pseudo-tensor categories, in particular, those admitting a combinatorial description with certain properties. We derive concrete general…

We extend the classification results for torsion classes and torsion-free classes in the category of finitely generated modules over a commutative noetherian ring to suitable symmetric monoidal closed noetherian abelian categories. Our main…

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion…

We set up a fibred categorical theory of obstruction and classification of morphisms that specializes to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further…

The analogy between Yetter's deformation theory form (lax) monoidal functors and Gerstenahaber's deformation theory for associative algebras is solidified by shown that under reasonable conditions the category of functors with an action of…

What are the fiber functors on small additive monoidal categories C which are not abelian? We give an answer which leads to a new Tannaka duality theorem for bialgebroids generalizing earlier results by Phung Ho Hai. The construction…

In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…

Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many…

For a topological space that is homeomorphic to a finite simplicial complex, we prove that the Bartels--Nikolaus assembly functor has a fully faithful right adjoint. Using this, we define for each such topological space $X$ a {\em Whitehead…

Let $\mathcal{A}$ and $\mathcal{B}$ be subcategories of tensor categories $\mathcal{C}$ and $\mathcal{D}$, respectively, both of which are abelian categories with finitely many isomorphism classes of simple objects. We prove that if their…

We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and…