Related papers: Derivator Six Functor Formalisms -- Definition and…
In this paper we present the notion of ``Deligne localized functors'', an avatar of the derived functors, whose definition is inspired by Deligne in [SGA 4,XVII]. Their definition involves the notions of Ind and Pro categories, they always…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These…
Variables are a crucial element in logic and are also addressed in institution theory, an effort to axiomatize logic. In institution theory, we typically use extensions (signature morphisms) obtained from variables instead of introducing…
Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…
We give a general construction of realization functors for $t$-structures on the base of a strong stable derivator. In particular, given such a derivator $\mathbb D$, a $t$-structure $\mathbf t=(\mathcal D^{\leq0},\mathcal D^{\geq0})$ on…
We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the corresponding deformation functor.
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…
A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…
The bicategorical point of view provides a natural setting for many concepts in the representation theory of monoidal categories. We show that centers of twisted bimodule categories correspond to categories of 2-dimensional natural…
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
Given a relation $R \subseteq I \times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result…
An (additive) functor F from an additive category A to an additive category B is said to be objective, provided any morphism f in A with F(f) = 0 factors through an object K with F(K) = 0. In this paper we concentrate on triangle functors…
This is mostly an overview. Given finitely presentable abelian categories $A$ and $B$, we sketch the construction of an abelian category of continuous functors from $A$ to $B$ that has nice $2$-categorical behaviour and gives an explicit…
Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…