4,472 research outputs found
On a New Construction of Pseudo BL-Algebras
We present a new construction of a class pseudo BL-algebras, called kite
pseudo BL-algebras. We start with a basic pseudo hoop . Using two injective
mappings from one set, , into the second one, , and with an identical
copy with the reverse order we construct a pseudo BL-algebra
where the lower part is of the form and the upper one is
. Starting with a basic commutative hoop we can obtain even a
non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with
non-commuting negations. We describe the construction, subdirect irreducible
kite pseudo BL-algebras and their classification
On a New Construction of Pseudo Effect Algebras
We define a new class of pseudo effect algebras, called kite pseudo effect
algebras, which is connected not necessarily with partially ordered groups, but
rather with generalized pseudo effect algebras where the greatest element is
not guaranteed. Starting even with a commutative generalized pseudo effect
algebra, we can obtain a non-commutative pseudo effect algebra. We show how
such kite pseudo effect algebras are tied with different types of the Riesz
Decomposition Properties. We find conditions when kite pseudo effect algebras
have the least non-trivial normal ideal.Comment: arXiv admin note: substantial text overlap with arXiv:1306.030
Kite Pseudo Effect Algebras
We define a new class of pseudo effect algebras, called kite pseudo effect
algebras, which is connected with partially ordered groups not necessarily with
strong unit. In such a case, starting even with an Abelian po-group, we can
obtain a noncommutative pseudo effect algebra. We show how such kite pseudo
effect algebras are tied with different types of the Riesz Decomposition
Properties. Kites are so-called perfect pseudo effect algebras, and we define
conditions when kite pseudo effect algebras have the least non-trivial normal
ideal
Polynomial functors from Algebras over a set-operad and non-linear Mackey functors
In this paper, we give a description of polynomial functors from (finitely
generated free) groups to abelian groups in terms of non-linear Mackey functors
generalizing those given in a paper of Baues-Dreckmann-Franjou-Pirashvili
published in 2001. This description is a consequence of our two main results: a
description of functors from (fi nitely generated free) P-algebras (for P a
set-operad) to abelian groups in terms of non-linear Mackey functors and the
isomorphism between polynomial functors on (finitely generated free) monoids
and those on (finitely generated free) groups. Polynomial functors from
(finitely generated free) P-algebras to abelian groups and from (finitely
generated free) groups to abelian groups are described explicitely by their
cross-e ffects and maps relating them which satisfy a list of relations.Comment: 58 page
Clifford Algebraic Remark on the Mandelbrot Set of Two--Component Number Systems
We investigate with the help of Clifford algebraic methods the Mandelbrot set
over arbitrary two-component number systems. The complex numbers are regarded
as operator spinors in D\times spin(2) resp. spin(2). The thereby induced
(pseudo) normforms and traces are not the usual ones. A multi quadratic set is
obtained in the hyperbolic case contrary to [1]. In the hyperbolic case a
breakdown of this simple dynamics takes place.Comment: LaTeX, 27 pages, 6 fig. with psfig include
Regular patterns, substitudes, Feynman categories and operads
We show that the regular patterns of Getzler (2009) form a 2-category biequivalent to the 2-category of substitudes of Day and Street (2003), and that the Feynman categories of Kaufmann and Ward (2013) form a 2-category biequivalent to the 2-category of coloured operads (with invertible 2-cells). These biequivalences induce equivalences between the corresponding categories of algebras. There are three main ingredients in establishing these biequivalences. The first is a strictification theorem (exploiting Power's General Coherence Result) which allows to reduce to the case where the structure maps are identity-on-objects functors and strict monoidal. Second, we subsume the Getzler and Kaufmann-Ward hereditary axioms into the notion of Guitart exactness, a general condition ensuring compatibility between certain left Kan extensions and a given monad, in this case the free-symmetric-monoidal-category monad. Finally we set up a biadjunction between substitudes and what we call pinned symmetric monoidal categories, from which the results follow as a consequence of the fact that the hereditary map is precisely the counit of this biadjunction
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