Titlebook: An Invitation to General Algebra and Universal Constructions; George M. Bergman Textbook 2015Latest edition Springer International Publish

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Free GroupsAs motivation for the general investigation of universal constructions, the concept of a free group on a set . is defined, and such groups are constructed in three ways: As sets of group-theoretic terms in . modulo consequences of the group identities, as subgroups of sufficiently large direct product groups, and as groups of reduced words.

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Varieties of AlgebrasWe at last formally define the concept of a (set-based) algebra, consider classes of algebras defined by families of identities (varieties), and prove Birkhoff’s . theorem. We devote several pages to Lie algebras. Clonal categories, and Lawvere’s Structure and Semantics functors, are briefly introduced.

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0172-5939 pen questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book..978-3-319-11477-4978-3-319-11478-1Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Root494

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Lattices, Closure Operators, and Galois Connectionsound, and as algebraic structures, and various completeness conditions they can satisfy are examined.Such structures often arise from . on sets, and this concept is developed.An insufficiently well known source of closure operators, which we develop, is the concept of a . between two sets. In the ca

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Universal Constructions in Category-Theoretic Termsctors, adjoint functors and limits and colimits; how one of these constructions can often be expressed in terms of another, and when such constructions exist. We prove such results as that limits always “respect” other limits, and colimits other colimits, and also examine special but important situa