G. Birkhoff and S. Mac Lane :
A survey of modern algebra .
Macmillan (New York ),
1941 .
The fiftieth anniversary of this book was commemorated in an article in Math. Intell. 14 :1 (1992) .
MR
0005093
Zbl
0061.04802
book
People
BibTeX
@book {key0005093m,
AUTHOR = {Birkhoff, Garrett and Mac Lane, Saunders},
TITLE = {A survey of modern algebra},
PUBLISHER = {Macmillan},
ADDRESS = {New York},
YEAR = {1941},
PAGES = {xi+450},
NOTE = {The fiftieth anniversary of this book
was commemorated in an article in \textit{Math.
Intell.} \textbf{14}:1 (1992). MR:0005093.
Zbl:0061.04802.},
}
S. Eilenberg and S. MacLane :
“Group extensions and homology ,”
Ann. Math. (2)
43 : 4
(October 1942 ),
pp. 757–831 .
MR
0007108
Zbl
0061.40602
article
People
BibTeX
@article {key0007108m,
AUTHOR = {Eilenberg, Samuel and MacLane, Saunders},
TITLE = {Group extensions and homology},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {43},
NUMBER = {4},
MONTH = {October},
YEAR = {1942},
PAGES = {757--831},
DOI = {10.2307/1968966},
NOTE = {MR:0007108. Zbl:0061.40602.},
ISSN = {0003-486X},
}
S. Eilenberg and S. MacLane :
“Natural isomorphisms in group theory ,”
Proc. Natl. Acad. Sci. U.S.A.
28 : 12
(December 1942 ),
pp. 537–543 .
See also article in Gaz. Mat. 29 :109–112 (1968) .
MR
0007421
Zbl
0061.09203
article
Abstract
People
BibTeX
Frequently in modern mathematics there occur phenomena of “naturality”: a “natural” isomorphism between two groups or between two complexes, a “natural” homeomorphism of two spaces and the like. We here propose a precise definition of the “naturality” of such correspondences, as a basis for an appropriate general theory. In this preliminary report we restrict ourselves to the natural isomorphisms of group theory; with this limitation we can present the basic concepts of our theory without developing the axiomatic approach necessary for a general treatment applicable to various branches of mathematics.
@article {key0007421m,
AUTHOR = {Eilenberg, Samuel and MacLane, Saunders},
TITLE = {Natural isomorphisms in group theory},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {28},
NUMBER = {12},
MONTH = {December},
YEAR = {1942},
PAGES = {537--543},
DOI = {10.1073/pnas.28.12.537},
NOTE = {See also article in \textit{Gaz. Mat.}
\textbf{29}:109--112 (1968). MR:0007421.
Zbl:0061.09203.},
ISSN = {0027-8424},
}
S. Eilenberg and S. MacLane :
“General theory of natural equivalences ,”
Trans. Am. Math. Soc.
58 : 2
(September 1945 ),
pp. 231–294 .
MR
0013131
Zbl
0061.09204
article
People
BibTeX
@article {key0013131m,
AUTHOR = {Eilenberg, Samuel and MacLane, Saunders},
TITLE = {General theory of natural equivalences},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {58},
NUMBER = {2},
MONTH = {September},
YEAR = {1945},
PAGES = {231--294},
DOI = {10.2307/1990284},
NOTE = {MR:0013131. Zbl:0061.09204.},
ISSN = {0002-9947},
}
S. MacLane :
“Groups, categories and duality ,”
Proc. Natl. Acad. Sci. U.S.A.
34 : 6
(June 1948 ),
pp. 263–267 .
MR
0025464
Zbl
0031.24702
article
BibTeX
@article {key0025464m,
AUTHOR = {MacLane, Saunders},
TITLE = {Groups, categories and duality},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {34},
NUMBER = {6},
MONTH = {June},
YEAR = {1948},
PAGES = {263--267},
DOI = {10.1073/pnas.34.6.263},
NOTE = {MR:0025464. Zbl:0031.24702.},
ISSN = {0027-8424},
}
S. MacLane :
“Duality for groups ,”
Bull. Am. Math. Soc.
56 : 6
(1950 ),
pp. 485–516 .
MR
0049192
Zbl
0045.29905
article
BibTeX
@article {key0049192m,
AUTHOR = {MacLane, Saunders},
TITLE = {Duality for groups},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {56},
NUMBER = {6},
YEAR = {1950},
PAGES = {485--516},
DOI = {10.1090/S0002-9904-1950-09427-0},
NOTE = {MR:0049192. Zbl:0045.29905.},
ISSN = {0002-9904},
}
S. Mac Lane :
Homology .
Die Grundlehren der mathematischen Wissenschaften 114 .
Academic Press (New York ),
1963 .
In German.
A Russian translation was published in 1966 .
MR
0156879
Zbl
0133.26502
book
BibTeX
@book {key0156879m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Homology},
SERIES = {Die Grundlehren der mathematischen Wissenschaften},
NUMBER = {114},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1963},
PAGES = {x+422},
NOTE = {In {G}erman. A Russian translation was
published in 1966. MR:0156879. Zbl:0133.26502.},
ISSN = {0072-7830},
}
S. Mac Lane :
“Natural associativity and commutativity ,”
Rice Univ. Stud.
49 : 4
(1963 ),
pp. 28–46 .
MR
0170925
Zbl
0244.18008
article
BibTeX
@article {key0170925m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Natural associativity and commutativity},
JOURNAL = {Rice Univ. Stud.},
FJOURNAL = {Rice University Studies},
VOLUME = {49},
NUMBER = {4},
YEAR = {1963},
PAGES = {28--46},
URL = {http://hdl.handle.net/1911/62865},
NOTE = {MR:0170925. Zbl:0244.18008.},
ISSN = {0035-4996},
}
S. MacLane :
“Categorical algebra ,”
Bull. Am. Math. Soc.
71 : 1
(1965 ),
pp. 40–106 .
MR
0171826
Zbl
0161.01601
article
BibTeX
@article {key0171826m,
AUTHOR = {MacLane, Saunders},
TITLE = {Categorical algebra},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {71},
NUMBER = {1},
YEAR = {1965},
PAGES = {40--106},
DOI = {10.1090/S0002-9904-1965-11234-4},
NOTE = {MR:0171826. Zbl:0161.01601.},
ISSN = {0002-9904},
}
S. Mac Lane :
“Foundations for categories and sets ,”
pp. 146–164
in
Category theory, homology theory and their applications
(Battelle Memorial Institute, Seattle, WA, 24 June–19 July 1968 ),
vol. II .
Edited by P. J. Hilton .
Lecture Notes in Mathematics 92 .
Springer (Berlin ),
1969 .
MR
0242919
Zbl
0218.18003
incollection
People
BibTeX
@incollection {key0242919m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Foundations for categories and sets},
BOOKTITLE = {Category theory, homology theory and
their applications},
EDITOR = {Hilton, Peter J.},
VOLUME = {II},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {92},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1969},
PAGES = {146--164},
DOI = {10.1007/BFb0080770},
NOTE = {(Battelle Memorial Institute, Seattle,
WA, 24 June--19 July 1968). MR:0242919.
Zbl:0218.18003.},
ISSN = {0075-8434},
ISBN = {9783540046110},
}
S. Mac Lane :
Categories for the working mathematician .
Graduate Texts in Mathematics 5 .
Springer (New York ),
1971 .
A German translation was published as Kategorien: Begriffssprache und mathematische Theorie (1972) .
MR
0354798
Zbl
0232.18001
book
BibTeX
@book {key0354798m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Categories for the working mathematician},
SERIES = {Graduate Texts in Mathematics},
NUMBER = {5},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1971},
PAGES = {ix+262},
NOTE = {A German translation was published as
\textit{Kategorien: Begriffssprache
und mathematische Theorie} (1972). MR:0354798.
Zbl:0232.18001.},
}
S. Mac Lane :
“Topology and logic as a source of algebra ,”
Bull. Am. Math. Soc.
82 : 1
(January 1976 ),
pp. 1–40 .
Retiring Presidential address.
MR
0414648
Zbl
0324.55001
article
BibTeX
@article {key0414648m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Topology and logic as a source of algebra},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {82},
NUMBER = {1},
MONTH = {January},
YEAR = {1976},
PAGES = {1--40},
DOI = {10.1090/S0002-9904-1976-13928-6},
NOTE = {Retiring Presidential address. MR:0414648.
Zbl:0324.55001.},
ISSN = {0002-9904},
}
S. Mac Lane :
Selected papers .
Edited by I. Kaplansky .
Springer (New York ),
1979 .
With contributions by Alfred Putnam, Roger Lyndon, Kaplansky, Samuel Eilenberg and Max Kelly.
MR
544841
Zbl
0459.01024
book
People
BibTeX
@book {key544841m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Selected papers},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1979},
PAGES = {xiii+556},
NOTE = {Edited by I. Kaplansky. With
contributions by Alfred Putnam, Roger
Lyndon, Kaplansky, Samuel Eilenberg
and Max Kelly. MR:544841. Zbl:0459.01024.},
ISBN = {9780387903941},
}
S. Mac Lane :
“A late return to a thesis in logic ,”
pp. 63–66
in
S. Mac Lane :
Selected papers .
Edited by I. Kaplansky .
Springer (New York ),
1979 .
incollection
People
BibTeX
@incollection {key99254301,
AUTHOR = {Mac Lane, Saunders},
TITLE = {A late return to a thesis in logic},
BOOKTITLE = {Selected papers},
EDITOR = {Irving Kaplansky},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1979},
PAGES = {63--66},
ISBN = {9780387903941},
}
S. Mac Lane :
Proof, truth and confusion ,
1982 .
The 1982 Ryerson Lecture, University of Chicago (1982).
misc
BibTeX
@misc {key19575965,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Proof, truth and confusion},
HOWPUBLISHED = {The 1982 Ryerson Lecture, University
of Chicago (1982)},
YEAR = {1982},
}
S. Mac Lane :
Mathematics, form and function .
Springer (New York ),
1986 .
MR
816347
Zbl
0675.00001
book
BibTeX
@book {key816347m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Mathematics, form and function},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1986},
PAGES = {xi+476},
DOI = {10.1007/978-1-4612-4872-9},
NOTE = {MR:816347. Zbl:0675.00001.},
ISBN = {9780387962177},
}
S. Mac Lane :
“Concepts and categories in perspective ,”
pp. 323–365
in
A century of mathematics in America ,
part I .
Edited by P. Duren, R. A. Askey, and U. C. Merzbach .
History of Mathematics 1 .
American Mathematical Society (Providence, RI ),
1988 .
An addendum to this article was published in History of Mathematics, part III (1989) .
MR
1003181
Zbl
0665.01002
incollection
People
BibTeX
@incollection {key1003181m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Concepts and categories in perspective},
BOOKTITLE = {A century of mathematics in {A}merica},
EDITOR = {Duren, Peter and Askey, Richard A. and
Merzbach, Uta C.},
VOLUME = {I},
SERIES = {History of Mathematics},
NUMBER = {1},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1988},
PAGES = {323--365},
NOTE = {An addendum to this article was published
in \textit{History of Mathematics, part~III}
(1989). MR:1003181. Zbl:0665.01002.},
ISSN = {0899-2428},
ISBN = {9780821801246},
}
S. Mac Lane and G. Birkhoff :
Algebra ,
3rd edition.
Chelsea (New York ),
1988 .
Republication of the {1967 original|MR:0214415}.
MR
941522
Zbl
0641.12001
book
People
BibTeX
@book {key941522m,
AUTHOR = {Mac Lane, Saunders and Birkhoff, Garrett},
TITLE = {Algebra},
EDITION = {3rd},
PUBLISHER = {Chelsea},
ADDRESS = {New York},
YEAR = {1988},
PAGES = {xx+626},
NOTE = {Republication of the {1967 original|MR:0214415}.
MR:941522. Zbl:0641.12001.},
ISBN = {9780828403306},
}
S. Mac Lane and I. Moerdijk :
Sheaves in geometry and logic: A first introduction to topos theory ,
reprinted edition.
Universitext .
Springer (New York ),
1994 .
MR
1300636
book
People
BibTeX
@book {key1300636m,
AUTHOR = {Mac Lane, Saunders and Moerdijk, Ieke},
TITLE = {Sheaves in geometry and logic: {A} first
introduction to topos theory},
EDITION = {reprinted},
SERIES = {Universitext},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1994},
PAGES = {xii+629},
NOTE = {MR:1300636.},
ISSN = {0172-5939},
ISBN = {9780387977102},
}
S. Mac Lane :
“Categories in geometry, algebra and logic ,”
Math. Japon.
42 : 1
(1995 ),
pp. 169–178 .
MR
1344646
Zbl
0831.18001
article
BibTeX
@article {key1344646m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Categories in geometry, algebra and
logic},
JOURNAL = {Math. Japon.},
FJOURNAL = {Mathematica Japonica},
VOLUME = {42},
NUMBER = {1},
YEAR = {1995},
PAGES = {169--178},
NOTE = {MR:1344646. Zbl:0831.18001.},
ISSN = {0025-5513},
CODEN = {MAJAA9},
}
S. Mac Lane :
“Mathematics at Göttingen under the Nazis ,”
Notices Am. Math. Soc.
42 : 10
(1995 ),
pp. 1134–1138 .
MR
1350011
Zbl
1042.01536
article
BibTeX
Read it here
@article {key1350011m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Mathematics at {G}\"ottingen under the
{N}azis},
JOURNAL = {Notices Am. Math. Soc.},
FJOURNAL = {Notices of the American Mathematical
Society},
VOLUME = {42},
NUMBER = {10},
YEAR = {1995},
PAGES = {1134--1138},
URL = {http://www.ams.org/notices/199510/maclane.pdf},
NOTE = {MR:1350011. Zbl:1042.01536.},
ISSN = {0002-9920},
CODEN = {AMNOAN},
}
S. Mac Lane :
“Samuel Eilenberg and categories ,”
pp. 127–131
in
Category theory 1999
(Coimbra, Portugal, 13–17 July 1999 ),
published as J. Pure Appl. Algebra
168 : 2–3 .
Issue edited by J. Adamek, P. T. Johnstone, and M. Sobral .
2002 .
MR
1887153
Zbl
0992.18001
incollection
People
BibTeX
@article {key1887153m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Samuel {E}ilenberg and categories},
JOURNAL = {J. Pure Appl. Algebra},
FJOURNAL = {Journal of Pure and Applied Algebra},
VOLUME = {168},
NUMBER = {2--3},
YEAR = {2002},
PAGES = {127--131},
DOI = {10.1016/S0022-4049(01)00092-5},
NOTE = {\textit{Category theory 1999} (Coimbra,
Portugal, 13--17 July 1999). Issue edited
by J. Adamek, P. T. Johnstone,
and M. Sobral. MR:1887153. Zbl:0992.18001.},
ISSN = {0022-4049},
CODEN = {JPAAA2},
}
S. Mac Lane :
Saunders Mac Lane: A mathematical autobiography .
A K Peters (Wellesley, MA ),
2005 .
With a preface by David Eisenbud.
MR
2141000
Zbl
1089.01010
book
People
BibTeX
@book {key2141000m,
AUTHOR = {Mac Lane, Saunders},
TITLE = {Saunders {M}ac {L}ane: {A} mathematical
autobiography},
PUBLISHER = {A K Peters},
ADDRESS = {Wellesley, MA},
YEAR = {2005},
PAGES = {xvi+358},
NOTE = {With a preface by David Eisenbud. MR:2141000.
Zbl:1089.01010.},
ISBN = {9781568811505},
}