Abstract and Concrete Categories: The Joy of Cats
Wiley, Apr 26, 1990 - Mathematics - 482 pages
A 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.
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Categories Functors and Natural Transformations
Objects and morphisms in abstract categories
15 other sections not shown
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A-morphism A-object algebraic amnestic arrow associated belongs called cartesian closed co-wellpowered cocomplete coequalizer colimits commutes complete composition concept concrete category concrete functor considered consisting construct COROLLARY correspondence defined DEFINITION denoted diagram discrete domain dual element embedding epimorphisms equalizer essentially EXAMPLES Exercise exists exists a unique fact factorization structure faithful faithful functor final finitary finite following conditions forgetful functor free objects full subcategory function functor G Galois given Hence hold hull identity Immediate implies initial injective isomorphism lift limits maps Math monadic mono-source morphism object ordered pair partial particular precisely preserves Proof Proposition Prove pullback quotient reflective subcategory regular regular epimorphisms relation REMARK representable resp retraction satisfies Show sink situation square strongly subobjects Theorem theory topological unique universal X-morphism