This paper investigates the univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then we present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify...

In this note we interpret Voevodsky’s Univalence Axiom in the language of (abstract) model categories. We then show that any posetal locally Cartesian closed model category Qt in which the mapping Hom(w)(Z × B,C) : Qt −→ Sets is functorial in Z and represented in Qt satisfies our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work was motivated by a question repo...

Let A be the class of all analytic functions f in the unit disc U = U(0, 1) normed with the conditions f(0) = 0 , f ′ (0) = 1. In this paper we give a sufficient condition for univalence which generalize the well known Becker’s criterion of univalence. 2000 Mathematical Subject Classification: 30C45

In [3], Breaz and Breaz gave an univalence condition of the integral operator Gn,α introduced in [2]. The purpose of this paper is to give univalence condition of the generalized integral operator Gn,m,α defined in [4]. Our results generalize the results of [3]. 2000 Mathematics Subject Classification: 30C45.

In [4], Breaz and Breaz gave the univalence conditions of the integral operator Fα,n of the analytic functions belonging to the classes T2, T2,μ and S(p). The purpose of this paper is to generalize the integral operator Fα,n by means of the generalized Al-Oboudi differential operator and investigate univalence conditions of this generalized integral operator considering the classes Tj , Tj,μ an...

In this paper, we investigate sufficient conditions for the univalence of an integral operator defined by generalized Al-Oboudi differential operator.

In this paper we define a general integral operator for analytic functions in the open unit disk and we determine some conditions for univalence of this integral operator.

Homotopy Type Theory promises a unification of the concepts of equality and equivalence in Type Theory, through the introduction of the univalence principle. However, existing proof assistants based on type theory treat this principle as an axiom, and it is not yet entirely clear how to extend them to handle univalence internally. In this paper, we propose a construction grounded on a univalent...

We study some integral operators and determine conditions for the univalence of these integral operators.

The aim of this paper is to obtain sufficient conditions for univalence of meromorphic functions in the U *. Also, we refine a quasiconformal extension criterion with the help of Becker's method. A number of univalence conditions would follow upon specializing the parameters involved in our main results. 1 Introduction We denote by U r = {z ∈ C : |z| < r} ( < r ≤ ) the disc of radius r and le...