He has tought at harvard, cornell and the university of chicago. According to our current online database, saunders mac lane has 42 students and 1815 descendants. Mac lane was born in norwich, connecticut, near where his family lived. Homology classics in mathematics saunders mac lane. Except for a few years in boston around age seven, saunders grew up in small towns, which it. He studied at yale university and then at the university of chicago and at goettingen, where he received the d. Mathematics form and function saunders maclane springer.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. Other readers will always be interested in your opinion of the books youve read. In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which i have had from all sides. Many are introduced not so much to be solved as to be tackled. His grandfather, william ward mclane was born in lewisville, pennsylvania in 1846, became a presbyterian minister but was forced to leave the. Mac lane s initial research was in logic and in algebraic.
Homology in presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which i have had from all sides. With sammy eilenberg, saunders mac lane was one of the original pioneers of category theory. Search for library items search for lists search for contacts search for a library. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 834 for the advisor id. Homology classics in mathematics saunders mac lane this classic and muchcited book is a systematic introduction to homological algebra, starting with basic notions in abstract algebra and category theory and continuing with an uptodate treatment of various advanced topics. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Discover book depositorys huge selection of saunders maclane books online. Buy homology by saunders maclane online at alibris.
Decker, the integral homology algebra of an eilenberg mac lane space, thesis, univ. Algebra maclane, saunders, birkhoff, garrett livres. The rejuvenation of algebra by the systematic use of the postulational method and the ideas and point of view of abstract group theory has been one of the crowning achievements of twentieth century. In 1945, they introduced the notion of category in a paper titled general theory of natural equivalences. In the process, eilenberg and mac lane created category theory. He studied at yale university and then at the university of chicago and at g6ttingen, where he received the d. Mac lane s initial research was in logic and in algebraic number theory valuation theory. Download pdf saunders mac lane free online new books. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Eilenberg was a member of bourbaki and, with henri cartan, wrote the 1956 book homological algebra. A topological space x has both homology and homotopy groups as invariants. Prove that the class of morphisms of a category is an abstract category, and conversely that the elements of any abstract category are the morphisms of a category if which is determined uniquely up to an isomorphism of categories. Saunders mac lane, who died on 14 april, was one of the few mathematicians to create a major new concept that has had a lasting effect on the subject.
Additional info for homology classics in mathematics sample text. An 1groupoid is an 1category where for all j, all jmorphisms are invertible up to higher morphisms. He initially worked on it as a language to enable natural transformations to be described in a natural way, and also developed, again with eilenberg many of the strong links. Saunders mac lane was an extraordinary mathematician, a dedicated teacher, and a good citizen who cared deeply about the values of science and education. Saunders mac lane the mathematics genealogy project. In his autobiography, he gives us a glimpse of his life and times, mixing the highly personal with professional observations. Garrett birkhoffharvard university saunders mac lane the university of chicago a survey of ern fourth. In garrett birkhoff and saunders mac lane published a survey of modern algebra. Prior to studying sets restricted in any way whateverfor instance, with operationsit will be necessary to consider sets in general and some notions about them. He studied at yale university and then at the university of chicago and at gottingen, where he received the d. Colin mclarty, the last mathematician from hilberts gottingen. By saunders mac lane oswald veblen, geometer and mathematical statesman, spanned in his career the full range of twentiethcentury mathematics in the united states. In presenting this treatment of homological algebra, it is a pleasure to acknowle. Saunders mac lane, born august 4, 1909, taftville, connecticut, u.
Homological algebra arose from many sources in algebra and topology. Bulletin of the american mathematical society 701964. Birkhoffmaclane algebra moderna pdf deviantart is the worlds largest online social community for artists. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems. Homology pdf by saunders maclane part of the classics in mathematics series. This is most interesting different take on mathematics by saunders maclane, whom, together with garrett birkhoff, also wrote an influential book on modern. Numerous and frequentlyupdated resource results are available from this search. This can be made precise in many ways, some of which are theorems, and. Saunders mac lane came from a scottish family who fled from scotland after the battle of culloden in 1746.
Abelian group factor algebra auditor cohomology collaboration commutative ring development group homological algebra homology proof sets topology. The homotopy hypothesis, due to grothendieck, says that 1groupoids are the same as homotopy types. This is a short obituary of saunders mac lane 19092005. Categories for the working mathematician wikipedia. If you have additional information or corrections regarding this mathematician, please use the update form. Saunders mac lane american mathematician britannica.