scholarly journals The Bicategory-Theoretic Solution of Recursive Domain Equations

2007 ◽  
Vol 172 ◽  
pp. 203-222
Author(s):  
Gian Luca Cattani ◽  
Marcelo P. Fiore
Keyword(s):  
Theoretic Solution ◽  
Recursive Domain Equations

scholarly journals The Category-Theoretic Solution of Recursive Domain Equations

1982 ◽  
Vol 11 (4) ◽  
pp. 761-783 ◽  
Author(s):  
M. B. Smyth ◽  
G. D. Plotkin
Keyword(s):  
Theoretic Solution ◽  
Recursive Domain Equations

scholarly journals The category-theoretic solution of recursive metric-space equations

2010 ◽  
Vol 411 (47) ◽  
pp. 4102-4122 ◽  
Author(s):  
Lars Birkedal ◽  
Kristian Støvring ◽  
Jacob Thamsborg
Keyword(s):  
Metric Space ◽  
Theoretic Solution

scholarly journals Learning Concepts: A Learning-Theoretic Solution to the Complex-First Paradox

2020 ◽  
Vol 87 (1) ◽  
pp. 135-151
Author(s):  
Nina L. Poth ◽  
Peter Brössel
Keyword(s):  
Theoretic Solution

scholarly journals Left semi-braces and solutions of the Yang–Baxter equation

2019 ◽  
Vol 31 (1) ◽  
pp. 241-263 ◽  
Author(s):  
Eric Jespers ◽  
Arne Van Antwerpen
Keyword(s):  
Positive Integer ◽  
Polynomial Identity ◽  
Baxter Equation ◽  
Polynomial Algebras ◽  
Finite Set ◽  
Theoretic Solution ◽  
Kirillov Dimension ◽  
Do So

Abstract Let {r\colon X^{2}\rightarrow X^{2}} be a set-theoretic solution of the Yang–Baxter equation on a finite set X. It was proven by Gateva-Ivanova and Van den Bergh that if r is non-degenerate and involutive, then the algebra {K\langle x\in X\mid xy=uv\text{ if }r(x,y)=(u,v)\rangle} shares many properties with commutative polynomial algebras in finitely many variables; in particular, this algebra is Noetherian, satisfies a polynomial identity and has Gelfand–Kirillov dimension a positive integer. Lebed and Vendramin recently extended this result to arbitrary non-degenerate bijective solutions. Such solutions are naturally associated to finite skew left braces. In this paper we will prove an analogue result for arbitrary solutions {r_{B}} that are associated to a left semi-brace B; such solutions can be degenerate or can even be idempotent. In order to do so, we first describe such semi-braces and then prove some decompositions results extending those of Catino, Colazzo and Stefanelli.

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