scholarly journals ON AUTOMORPHISMS OF CATEGORIES OF UNIVERSAL ALGEBRAS

2007 ◽  
Vol 17 (05n06) ◽  
pp. 1115-1132 ◽  
Author(s):  
BORIS PLOTKIN ◽  
GRIGORI ZHITOMIRSKI
Keyword(s):  
Forgetful Functor ◽  
Universal Algebras ◽  
Categories Of Universal Algebras

Let [Formula: see text] be a variety of universal algebras. We suggest an approach for describing automorphisms of a category [Formula: see text] of free [Formula: see text]-algebras. In particular, this approach allows us to answer the question: is an automorphism of such a category inner? Most of the results actually deal with arbitrary categories supplied with a represented forgetful functor.

scholarly journals Duality in topological algebra

1978 ◽  
Vol 18 (3) ◽  
pp. 475-480 ◽  
Author(s):  
B.J. Day
Keyword(s):  
Topological Algebra ◽  
Forgetful Functor ◽  
Finite Product ◽  
Universal Algebras ◽  
Basic Set ◽  
Totally Disconnected

Aspects of duality relating to compact totally disconnected universal algebras are considered. It is shown that if P is a ““basic“ set of injectives in a variety of compact totally disconnected algebras then the category P of P-copresentable objects is in duality with the class of all G-copresentable algebras on P, where G: P → Ens is the forgetful functor and an algebra is taken to mean a finite-product-preserving functor from P to Ens.

Weak Products of Simple Universal Algebras

1969 ◽  
Vol 42 (1-3) ◽  
pp. 157-171 ◽  
Author(s):  
Tah-Kai Hu
Keyword(s):  
Universal Algebras

WHITEHEAD EXACT SEQUENCE AND DIFFERENTIAL GRADED FREE LIE ALGEBRA

2004 ◽  
Vol 15 (10) ◽  
pp. 987-1005 ◽  
Author(s):  
MAHMOUD BENKHALIFA
Keyword(s):  
Exact Sequence ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Integral Domain ◽  
Free Lie Algebra ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Equivalent Class

Let R be a principal and integral domain. We say that two differential graded free Lie algebras over R (free dgl for short) are weakly equivalent if and only if the homologies of their corresponding enveloping universal algebras are isomophic. This paper is devoted to the problem of how we can characterize the weakly equivalent class of a free dgl. Our tool to address this question is the Whitehead exact sequence. We show, under a certain condition, that two R-free dgls are weakly equivalent if and only if their Whitehead sequences are isomorphic.

Varieties of infinitary universal algebras

1985 ◽  
Vol 20 (1) ◽  
pp. 123-126
Author(s):  
Ji?� Rosick�
Keyword(s):  
Universal Algebras

scholarly journals Universal algebras with all operations of bounded range

1974 ◽  
Vol 30 (2) ◽  
pp. 177-185 ◽  
Author(s):  
I. G. Rosenberg
Keyword(s):  
Universal Algebras
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