Related papers: Non-additive functors and Euler characteristics

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective…

The notion of essential submodules and essential extensions of modules are extended to groups (typically nonabelian), and several necessary and sufficient conditions for a group to possess a proper essential subgroup are investigated.…

We give an exposition of the theory of adjoints and conductors for curves on nonsingular surfaces, emphasizing the case of plane curves, for which the presentation is particularly elementary. This is closely related to Max Noether's…

Taking symmetric powers of varieties can be seen as a functor from the category of varieties to the category of varieties with an action by the symmetric group. We study a corresponding map between the Grothendieck groups of these…

We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matrices. We then study counting functions associated to these…

To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common…

A general construction of Knop creates a symmetric monoidal category $\mathcal{T}(\mathcal{A},\delta)$ from any regular category $\mathcal{A}$ and a fixed degree function $\delta$. A special case of this construction are the Deligne…

There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to…

Morphisms in the linear category A of Jacobi diagrams in handlebodies give rise to interesting contravariant functors on the category gr of finitely-generated free groups, encoding part of the composition structure of the category A. These…

This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…

A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of…

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 develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification…

This paper explores differential bundles in tangent categories, characterizing them as functors from a structure category. This is analogous to the actegory perspective of Garner and Leung, which we also use to describe the tangent…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

In this paper we will prove that there exists a covariant functor, called algebraic anabelian functor, from the category of algebraic schemes over a given field to the category of outer homomorphism sets of groups. The algebraic anabelian…

We develop a theory of curved A-infinity-categories around equivalences of their module categories. This allows for a uniform treatment of curved and uncurved A-infinity-categories which generalizes the classical theory of uncurved…

We study the relation between additivity and deduction theorems in the algebraic semantics of congruential modal logic. Additivity of the modal operator is well-known to imply the local deduction-detachment theorem. Our main theme is that…

We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such…