Results 1 to 10 of about 28,174 (201)
Bicategories in univalent foundations [PDF]
Mathematical Structures in Computer Science, 2021 AbstractWe develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of univalent bicategories in a modular fashion, we develop displayed bicategories, an analog of displayed 1-categories introduced
Benedikt Ahrens +4 more
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Univalency of Certain Transform of Univalent Functions
Proceedings of the Bulgarian Academy of Sciences, 2023 We consider univalency problem in the unit disc $$\mathbb{D}$$ of the function \[g(z)=\frac{(z/f(z))-1}{-a_{2}}, \] where $$f$$ belongs to some classes of univalent functions in $$\mathbb{D}$$ and $$a_{2}=\frac{f''(0)}{2}\neq 0$$.
Obradović, Milutin, Tuneski, Nikola
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The Marriage of Univalence and Parametricity [PDF]
Journal of the ACM, 2021 Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, which are frequently used to mechanize mathematical results and carry out program verification efforts, equality is appallingly syntactic, and as a result, exploiting equivalences is cumbersome at best ...
Tabareau, Nicolas +2 more
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Mathematische Annalen, 2017 We review the concept of a univalent fibration and show by elementary means that every Kan fibration in simplicial sets can be embedded in a univalent Kan fibration.
van den Berg, B., Moerdijk, I.
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Univalence Criteria for Locally Univalent Analytic Functions
Ukrainian Mathematical Journal, 2023 UDC 517.5 Suppose that p ( z ) = 1 + z ϕ ' ' ( z ) / ϕ ' ( z ) , where ϕ ( z ) is a locally univalent analytic function in the unit disk D with ϕ ( 0 ) = ϕ ' ( 1 ) - 1 = 0. We establish the lower and upper bounds for the best constants σ 0
Zhenyong Hu, Jinhua Fan, Xiaoyuan Wang
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Annals of Pure and Applied Logic, 2020 Corrected typos, updated references and added a section on Church's ...
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The Univalence of an Integral [PDF]
Proceedings of the American Mathematical Society, 1971 Let f ( z ) f(z) be a normalized function, analytic and univalent in the open unit disc. It is shown that if g ( z ) = ∫ 0 z ( f ( t
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Decomposing the Univalence Axiom [PDF]
arXiv: Logic in Computer Science, 2017 This paper investigates Voevodsky's univalence axiom in intensional Martin-L f 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 present a new decomposition of the univalence axiom into simpler axioms.
Orton, Ian, Pitts, Andrew M.
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Univalence for convolutions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1996 The radius of univalence is found for the convolution f∗g of functions f ∈ S (normalized univalent functions) and g ∈ C (close‐to‐convex functions). A lower bound for the radius of univalence is also determined when f and g range over all of S. Finally, a characterization of C provides an inclusion relationship.
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On Univalent Polynomials [PDF]
Proceedings of the American Mathematical Society, 1976 We define V n ⊆ C n − 1 {V_n} \subseteq {{\mathbf {C}}^{n - 1}} to be the set of ( n −
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