Combinational, algebraic and topological representations of groups, semigroups and categories

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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the rea…

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Title Statements

Full title :Combinational, algebraic and topological representations of groups, semigroups and categories / Ales̆ Pultr, Vĕra Trnková.

Summary

Edition Statements

Publication Date:1980.

Publication Statements

Publisher(s):North-Holland Pub. Co
Place of Publication:Amsterdam
Language:eng
Publication Date:1980.

The Physical Object

Description:1 online resource (vi, 372 pages) : : illustrations.

Edition Identifiers

ISBN:9780080954288, 0080954286
oclc:ocn649907805
LC Classification:QA164
Dewey Decimal:512.22

Front Cover; Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories; Copyright Page; Preface; Contents; Introduction; Chapter I. Preliminaries; 1. Relations, algebraic operations, homomorphisms; 2. Monoids and concrete monoids; 3. Categories, functors, transformations; 4. Concrete categories; 5. Some important concrete categories; 6. Embeddings; 7. Two easy but important embeddings; 8. The representation problems; 9. Bibliographical remarks; Chapter II. Basic Embeddings; 1. Three obvious realizations; 2. Two important extensions.

3. Rigid binary relations4. Rigid symmetric binary relations; 5. Graph is alg-universal. Consequences; 6. Assumption (M) and strong embedding of S(P- ) into Graph; 7. Strong embedding of S(P+) into S(P- ); 8. Bibliographical remarks; Chapter III. Universality of S(P+); 1. Strong embedding of S(P+, . . ., P+) into S(P+); 2. Representations of thin categories; 3. Categories I(F; (T, <=)) and realizations of concrete categories; 4. S(P+) is universal; 5. Bibliographical remarks; Chapter IV. Combinatorics; 1. Graphs, symmetric graphs, undirected graphs.

2. The "arrow construction" in its simplest form3. Two application…