LEADER 04359nam 22006375 450 001 9910254294503321 005 20200705030509.0 010 $a3-319-41917-X 024 7 $a10.1007/978-3-319-41917-6 035 $a(CKB)3710000001041180 035 $a(DE-He213)978-3-319-41917-6 035 $a(MiAaPQ)EBC6310775 035 $a(MiAaPQ)EBC5576693 035 $a(Au-PeEL)EBL5576693 035 $a(OCoLC)1066186161 035 $a(PPN)198341326 035 $a(EXLCZ)993710000001041180 100 $a20170106d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to the Language of Category Theory /$fby Steven Roman 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XII, 169 p. 176 illus., 5 illus. in color.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 311 $a3-319-41916-1 320 $aIncludes bibliographical references and index. 327 $aPreface -- Categories -- Functors and Natural Transformations -- Universality -- Cones and Limits -- Adjoints -- References -- Index of Symbols -- Index. 330 $aThis textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. The first chapter of the book introduces the definitions of category and functor and discusses diagrams, duality, initial and terminal objects, special types of morphisms, and some special types of categories, particularly comma categories and hom-set categories. Chapter 2 is devoted to functors and natural transformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions ? products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts. 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 14$aCategory Theory, Homological Algebra. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 615 24$aGeneral Algebraic Systems. 676 $a512.62 700 $aRoman$b Steven$4aut$4http://id.loc.gov/vocabulary/relators/aut$057255 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254294503321 996 $aIntroduction to the language of category theory$91560436 997 $aUNINA