000			01827nam a22002297a 4500
003			OSt
005			20220329093347.0
008			130109b xxu||||| |||| 00| 0 eng d
020			_a0521010608
040			_ctshering
082			_a511.322 WILL
100			_aLawvere, F. William.
245			_aSets for mathematics / _cF W Lawvere; Robert Rosebrugh
260			_aNew York : _bCambridge University Press, _c2003.
300			_axiii, 261 p. : _bill. ; _c25.3 cm.
504			_aIncludes bibliography and index.
520			_aAdvanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape
650			_aSet thoery.
650			_aMATHEMATICS _vSet Theory.
700			_aRosebrugh, Robert.
942			_2ddc _cBK
999			_c6534 _d6534