Sheaves in Geometry and Logic: A First Introduction to Topos Theory

Front Cover
Springer Science & Business Media, 1992 - Mathematics - 627 pages
5 Reviews
We dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death. This has cast a shadow on our subsequent work. Our views of topos theory, as presented here, have been shaped by continued study, by conferences, and by many personal contacts with friends and colleagues-including especially O. Bruno, P. Freyd, J.M.E. Hyland, P.T. Johnstone, A. Joyal, A. Kock, F.W. Lawvere, G.E. Reyes, R Solovay, R Swan, RW. Thomason, M. Tierney, and G.C. Wraith. Our presentation combines ideas and results from these people and from many others, but we have not endeavored to specify the various original sources. Moreover, a number of people have assisted in our work by pro viding helpful comments on portions of the manuscript. In this respect, we extend our hearty thanks in particular to P. Corazza, K. Edwards, J. Greenlees, G. Janelidze, G. Lewis, and S. Schanuel.
  

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Contents

II
1
III
10
IV
24
V
29
VI
31
VII
35
VIII
39
IX
44
LXII
296
LXIII
302
LXIV
315
LXV
318
LXVI
324
LXVII
331
LXVIII
343
LXIX
347

X
48
XI
50
XII
57
XIII
62
XIV
64
XV
65
XVI
69
XVII
73
XVIII
79
XIX
83
XX
88
XXI
95
XXII
97
XXIII
99
XXIV
103
XXV
106
XXVI
109
XXVII
116
XXVIII
121
XXIX
128
XXX
134
XXXI
140
XXXII
145
XXXIII
150
XXXIV
155
XXXV
161
XXXVI
167
XXXVII
171
XXXVIII
176
XXXIX
180
XL
184
XLI
190
XLII
198
XLIII
204
XLIV
210
XLV
213
XLVI
218
XLVII
219
XLVIII
223
XLIX
227
L
233
LI
235
LII
237
LIII
240
LIV
247
LV
256
LVI
263
LVII
267
LVIII
268
LIX
277
LX
284
LXI
291
LXX
348
LXXI
353
LXXII
361
LXXIII
366
LXXIV
378
LXXV
384
LXXVI
390
LXXVII
394
LXXVIII
399
LXXIX
409
LXXX
416
LXXXI
421
LXXXII
422
LXXXIII
425
LXXXIV
434
LXXXV
436
LXXXVI
439
LXXXVII
447
LXXXVIII
452
LXXXIX
457
XC
468
XCI
472
XCII
473
XCIII
475
XCIV
477
XCV
482
XCVI
489
XCVII
493
XCVIII
502
XCIX
508
C
513
CI
516
CII
521
CIII
523
CIV
528
CV
529
CVI
532
CVII
535
CVIII
541
CIX
555
CX
561
CXI
568
CXII
571
CXIII
574
CXV
577
CXVI
580
CXVII
589
CXVIII
598
CXIX
605
CXX
615
CXXI
619
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About the author (1992)

Biography of Saunders Mac Lane

Saunders Mac Lane was born on August 4, 1909 in Connecticut. He studied at Yale University and then at the University of Chicago and at Gttingen, where he received the D.Phil. in 1934. He has tought at Harvard, Cornell and the University of Chicago.

Mac Lane's initial research was in logic and in algebraic number theory (valuation theory). With Samuel Eilenberg he published fifteen papers on algebraic topology. A number of them involved the initial steps in the cohomology of groups and in other aspects of homological algebra - as well as the discovery of category theory. His famous and undergraduate textbook Survey of modern algebra, written jointly with G. Birkhoff, has remained in print for over 50 years. Mac Lane is also the author of several other highly successful books.

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