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classes of algebras
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Classes of algebras are of two types: either classes of specific algebras, such as: group algebras, K-algebras, groupoid algebras, logic algebras, and so on, or general ones, such as general classes of: categorical algebras, higher dimensional algebra (HDA), supercategorical algebras, universal algebras, and so on.
Remarks With the above definition, one can also define a category of classes of algebras and their associated groupoid homomorphisms which is then an algebraic category.
Although all classes can be regarded as equivalence, weak equivalence, etc., classes of algebras (either specific or general ones), do not define identical, or even isomorphic structures, as the notion of `equivalence' can have more than one meaning even in the algebraic case.
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"classes of algebras" is owned by bci1.
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Cross-references: structures, isomorphic, even, weak equivalence, equivalence, groupoid homomorphisms, category, groupoid category, object, algebraic, universal algebras, supercategorical algebras, HDA, higher dimensional algebra, categorical algebras, logic algebras, groupoid, group algebras, classes, types
There are 77 references to this entry.
This is version 21 of classes of algebras, born on 2008-07-23, modified 2008-09-18.
Object id is 10855, canonical name is ClassesOfAlgebras.
Accessed 935 times total.
Classification:
| AMS MSC: | 08A70 (General algebraic systems :: Algebraic structures :: Applications of universal algebra in computer science) | | | 08A05 (General algebraic systems :: Algebraic structures :: Structure theory) | | | 18E05 (Category theory; homological algebra :: Abelian categories :: Preadditive, additive categories) | | | 18-00 (Category theory; homological algebra :: General reference works ) |
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