Regular functors and relative realisability categories

2013 ◽  
Vol 23 (5) ◽  
pp. 1082-1110
Author(s):  
WOUTER PIETER STEKELENBURG
Keyword(s):  
Universal Property ◽  
Arbitrary Base ◽  
Geometric Morphisms

The relative realisability toposes introduced by Awodey, Birkedal and Scott in Awodey et al. (2002) satisfy a universal property involving regular functors to other categories. We use this universal property to define what relative realisability categories are when they are based on categories other than the topos of sets. This paper explains the property and gives a construction for relative realisability categories that works for arbitrary base Heyting categories. The universal property also provides some new geometric morphisms to relative realisability toposes.

Flat functors and classifying toposes

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
General Theory ◽  
Geometric Theory ◽  
Small Category ◽  
Independent Interest ◽  
Yoneda Lemma ◽  
Geometric Morphisms ◽  
The Way

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.

Regular Hom-algebras admitting a multiplicative basis

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio J. Calderón Martín
Keyword(s):  
Arbitrary Dimension ◽  
Base Field ◽  
Direct Sum ◽  
Multiplicative Basis ◽  
Arbitrary Base ◽  
The Family

AbstractLet {({\mathfrak{H}},\mu,\alpha)} be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field {{\mathbb{F}}}. A basis {{\mathcal{B}}=\{e_{i}\}_{i\in I}} of {{\mathfrak{H}}} is called multiplicative if for any {i,j\in I}, we have that {\mu(e_{i},e_{j})\in{\mathbb{F}}e_{k}} and {\alpha(e_{i})\in{\mathbb{F}}e_{p}} for some {k,p\in I}. We show that if {{\mathfrak{H}}} admits a multiplicative basis, then it decomposes as the direct sum {{\mathfrak{H}}=\bigoplus_{r}{{\mathfrak{I}}}_{r}} of well-described ideals admitting each one a multiplicative basis. Also, the minimality of {{\mathfrak{H}}} is characterized in terms of the multiplicative basis and it is shown that, in case {{\mathcal{B}}}, in addition, it is a basis of division, then the above direct sum is composed by means of the family of its minimal ideals, each one admitting a multiplicative basis of division.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

Generating fixed density bracelets of arbitrary base

2013 ◽  
Vol 91 (3) ◽  
pp. 434-446 ◽  
Author(s):  
S. Karim ◽  
Z. Alamgir ◽  
S. M. Husnine
Keyword(s):  
Arbitrary Base

scholarly journals Parametrizing quartic algebras over an arbitrary base

2011 ◽  
Vol 5 (8) ◽  
pp. 1069-1094 ◽  
Author(s):  
Melanie Wood
Keyword(s):  
Arbitrary Base

scholarly journals ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS

2013 ◽  
Vol 56 (1) ◽  
pp. 57-63
Author(s):  
CRISTIAN VIRDOL
Keyword(s):  
Finite Order ◽  
Modular Forms ◽  
Number Fields ◽  
Base Change ◽  
Hilbert Modular Forms ◽  
Special Values ◽  
Finite Dimensional ◽  
Arbitrary Base ◽  
Hilbert Modular

AbstractIn this paper we generalize some results, obtained by Shimura, on the special values of L-functions of l-adic representations attached to quadratic CM-base change of Hilbert modular forms twisted by finite order characters. The generalization is to the case of the special values of L-functions of arbitrary base change to CM-number fields of l-adic representations attached to Hilbert modular forms twisted by some finite-dimensional representations.

scholarly journals On the Structure of Graded Leibniz Algebras

2015 ◽  
Vol 22 (01) ◽  
pp. 83-96 ◽  
Author(s):  
Antonio J. Calderón Martín ◽  
José M. Sánchez Delgado
Keyword(s):  
Arbitrary Dimension ◽  
Unit Element ◽  
Homogeneous Component ◽  
Maximal Length ◽  
Base Field ◽  
Leibniz Algebras ◽  
Arbitrary Base

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form [Formula: see text] with U a subspace of 𝔏1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of 𝔏, satisfying [Ij, Ik]=0 if j ≠ k. In the case of 𝔏 being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.

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