Related papers: A Pirashvili-type theorem for functors on non-empt…

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…

We initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We show that, when there are enough projectives or enough injectives,…

We give in this paper an isomorphism theorem between derived functors over categories of modules.There is a nice class of categories that gives examples in which this theorem applies for a special construction. This leads us to a new…

We show under suitable finiteness conditions that a functor between abelian categories induces a (not necessarily additive) map between their Grothendieck groups. This is related to the derived functors of Dold and Puppe, and generalizes a…

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…

We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…

Reflexive homology and dihedral homology are the homology theories associated to the reflexive and dihedral crossed simplicial groups respectively. The former has recently been shown to capture interesting information about…

We show that Bondal-Orlov's reconstruction theorem holds in noncommutative projective geometry. We also prove that fully faithful exact functors between derived categories of noncommutative projective schemes are of Fourier-Mukai type.

We develop an approach to Goodwillie's calculus of functors using the techniques of higher topos theory. Central to our method is the introduction of the notion of fiberwise orthogonality, a strengthening of ordinary orthogonality which…

Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relationship with torsion theories, Galois theory, homology and factorisation systems. It is shown how…

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…

We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefschetz fixed-morphism theorem. In order to do so, we use the…

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.

We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological version of the classical AKSZ field theories that occur in…

In this article we study cohomological properties of the category of polynomial outer functors on free groups, which are the functors from the category of finitely generated free groups to the category of rational vector spaces which send…

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 prove that Ringel duality in the category of strict polynomial functors can be interpreted as derived functors of non-additive functors (in the sense of Dold and Puppe). We give applications of this fact for both theories.

Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is…

G\'en\'eralisant un article de Pirashvili, nous caract\'erisons les petites cat\'egories additives A telles que l'inclusion dans la cat\'egorie des foncteurs de A vers les groupes ab\'eliens de la sous-cat\'egorie pleine des foncteurs…