Abstract and Concrete Categories: The Joy of CatsA modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises. |
Contents
Introduction | 1 |
Categories Functors and Natural Transformations | 11 |
Objects and morphisms in abstract categories | 91 |
Copyright | |
16 other sections not shown
Other editions - View all
Abstract and Concrete Categories: The Joy of Cats Jiri Adamek,Horst Herrlich,George E. Strecker No preview available - 2009 |
Common terms and phrases
A-object A-reflection adjoint functor adjoint situation amnestic called cartesian closed co-adjoint co-wellpowered cocomplete codomain coequalizer colimits commutes concrete category concrete category A,U concrete functor concretely isomorphic conditions are equivalent considered construct coproducts coreflective coseparator defined DEFINITION diagram dual epi-sink epireflective essentially algebraic EXAMPLES exists a unique extremal epimorphisms extremal monomorphism factorization structure faithful faithful functor fibre-small finitary finite following conditions forgetful functor free objects full concrete full subcategory function functor G G-structured Galois correspondence HComp Hence hom(A homomorphisms implies initial injective hull injective objects isomorphism-closed Let A,U lift limits maps Math monadic mono-source natural transformation numbers pair poset precisely preserves Proof Proposition pullback quotient reflective subcategory regular epimorphisms regular monomorphisms resp retraction Show strongly complete structured arrow subobjects surjective terminal object Theorem topological category topological spaces topologically algebraic wellpowered X-morphism