Related papers: Taylor Morphisms
We study versions of Goodwillie's calculus of functors for indexing diagrams other than cubes. We in particular construct universal excisive approximations for a larger class of diagrams, which yields an extension of the Taylor tower. We…
Three categories of algebras with morphisms generalising the usual set of algebra homomorphisms are described. The Sweedler product provides a hom-tensor equivalence relating these three categories, and a tool enabling the universal…
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
Let $D$ be the open unit disc in the complex plane. We denote by $\mathbb{C}$ the set of complex numbers and consider any compact set $K$ which is disjoint from $D$ and which also has connected complement. Let $A(K)$ denote all the…
In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…
In this paper we discuss generalizations of discrete torsion to noninvertible symmetries in 2d QFTs. One point of this paper is to explain that there are two complementary generalizations. Both generalizations are counted by $H^2(G,U(1))$…
The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…
We derive the Taylor polynomial of a function, which is $m$-times continuously differentiable and positive homogeneous of order $m$. The Taylor polynomial in $a$ for $f(b)$ of order $m$ in general is a polynomial of order $m$ in $b-a$. If…
The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of…
In this article, we introduce fundamental notions and results about pullback formalisms, building on work of Drew-Gallauer. Our main application is producing a pullback formalism $\mathbf{SH}^{\mathrm{hol}}$ that encodes a version of…
Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…
Eventually after Dieudonn\'e-Grothendieck, we give intrinsic definitions of \'etale, lisse and non-ramifi\'e morphisms for general adic rings and general locally convex rings. And we investigate the corresponding \'etale-like, lisse-like…
We prove the existence of holomorphic functions $f$ defined on any open convex subset ${\rm \Omega}\subset {{\mathbb C}}^n$, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact…
We prove simultaneous Universal Approximation of a certain type of Pade Approximants and of Taylor series with the same indexes. This is a generic phenomenon in the space of holomorphic functions in any simply connected domain, as well as…
We extend the holomorphic analytic torsion classes of Bismut and K\"ohler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the…
A closed 3-form $H \in \Omega^3_0(M)$ defines an extension of $\Gamma(TM)$ by $\Omega^2_0(M)$. This fact leads to the definition of the group of $H$-twisted Hamiltonian symmetries $\Ham(M, \JJ; H)$ as well as Hamiltonian action of Lie group…
In this paper, usual Sturm-Liouville problems are extended for symmetric functions so that the corresponding solutions preserve the orthogonality property. Two basic examples, which are special cases of a generalized Sturm-Liouville…
Given a scheme S and a flat morphism T \to S of finite presentation we define a surjective S-morphism to an {\'e}tale and separated S-scheme, which is universal in an obvious sense. Properties of this morphism are deduced from a thorough…
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…
We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…