Related papers: Derived smooth induction with applications
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining…
A model structure is defined on the category of derived differentiable schemes, and it is used to analyse the truncation 2-functor from derived manifolds to d-manifolds. It is proved that the induced 1-functor between the homotopy…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
In this paper, we generalise the construction of the functorial pullback of refined unramified cohomology between smooth schemes, by following the ideas of Fulton's intersection theory and Rost's cycle modules. We also define standard…
Suppose that $\mathcal{A}$ is an abelian category whose derived category $\mathcal{D}(\mathcal{A})$ has $Hom$ sets and arbitrary (small) coproducts, let $T$ be a (not necessarily classical) ($n$-)tilting object of $\mathcal{A}$ and let…
Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to investigate basic operations such as direct sum, splitting, and…
We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With…
In this paper, we will construct the injective resolution of any $\cR$-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in ($\cR$-2-Mod).
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
The presence of non-convexity in smooth optimization problems arising from deep learning have sparked new smoothness conditions in the literature and corresponding convergence analyses. We discuss these smoothness conditions, order them,…
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…