03358nam 22006492 450 991081565250332120151005020622.01-107-23842-01-299-39995-91-107-33277-X1-107-33689-91-139-54233-81-107-33357-11-107-33523-X1-107-33606-6(CKB)3460000000128975(SSID)ssj0000832914(PQKBManifestationID)11476935(PQKBTitleCode)TC0000832914(PQKBWorkID)10935475(PQKB)10339432(UkCbUP)CR9781139542333(MiAaPQ)EBC1139621(Au-PeEL)EBL1139621(CaPaEBR)ebr10667768(CaONFJC)MIL471245(OCoLC)830001169(PPN)26130559X(EXLCZ)99346000000012897520120702d2013|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierCoherence in three-dimensional category theory /Nick Gurski, University of Sheffield[electronic resource]Cambridge :Cambridge University Press,2013.1 online resource (vii, 278 pages) digital, PDF file(s)Cambridge tracts in mathematics ;201Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-03489-2 1-107-32713-X Includes bibliographical references and index.Introduction -- Background: Bicategorical background ; Coherence for bicategories ; Gray-categories -- Tricategories: The algebraic definition of tricategory ; Examples ; Free constructions ; Basic structure ; Gray-categories and tricategories ; Coherence via Yoneda ; Coherence via free constructions -- Gray-monads: Codescent in Gray-categories ; Codescent as a weighted colimit ; Gray-monads and their algebras ; The reflection of lax algebras into strict algebras ; A general coherence result.Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.Cambridge tracts in mathematics ;201.TricategoriesTricategories.512/.55MAT018000bisacshGurski Nick1980-1686990UkCbUPUkCbUPBOOK9910815652503321Coherence in three-dimensional category theory4060117UNINA