LEADER 01122nam0 2200265 450 001 000020310 005 20081204124652.0 100 $a20081204d1970----km-y0itay50------ba 101 0 $aeng 102 $aDE 105 $ay-------001yy 200 1 $aReport on the Symposium on coastal Geodesy$d=Rapport sur le Symposium de Géodésie cotière$ehelt in Munich 20th-24th July 1970$e=tenu a Munich 20-24 juillet 1970$fedited by Rudolf Sigl 210 $aMunich$cInstitute for astronomical and physical Geodesy$d1970 215 $a644 p.$ctab., fig.$d30 cm 300 $aIn testa al front.: International Union of Geodesy and Geophysics=Union geodesique et geophysique internationale 500 10$aReport on the Symposium on coastal Geodesy$933453 610 1 $aGeodesia costiera$aCongressi 676 $a526.1$v20$9Geodesia 702 1$aSigl,$bRudolf 710 12$aSymposium on coastal Geodesy$e$0632566 801 0$aIT$bUNIPARTHENOPE$c20081204$gRICA$2UNIMARC 912 $a000020310 951 $aG 526.3/1$bG s.i.$cDSA$d2008 996 $aReport on the Symposium on coastal Geodesy$933453 997 $aUNIPARTHENOPE LEADER 06535nam 22006855 450 001 9910962003503321 005 20250806181158.0 010 $a9781461209270 010 $a1461209277 024 7 $a10.1007/978-1-4612-0927-0 035 $a(CKB)3400000000089325 035 $a(SSID)ssj0000808475 035 $a(PQKBManifestationID)11429842 035 $a(PQKBTitleCode)TC0000808475 035 $a(PQKBWorkID)10778289 035 $a(PQKB)11609920 035 $a(DE-He213)978-1-4612-0927-0 035 $a(MiAaPQ)EBC3074007 035 $a(PPN)237993708 035 $a(EXLCZ)993400000000089325 100 $a20121227d1994 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSheaves in Geometry and Logic $eA First Introduction to Topos Theory /$fby Saunders MacLane, Ieke Moerdijk 205 $a1st ed. 1994. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1994. 215 $a1 online resource (XII, 630 p.) 225 1 $aUniversitext,$x2191-6675 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780387977102 311 08$a0387977104 320 $aIncludes bibliographical references and indexes. 327 $aPrologue -- Categorial Preliminaries -- I. Categories of Functors -- 1. The Categories at Issue -- 2. Pullbacks -- 3. Characteristic Functions of Subobjects -- 4. Typical Subobject Classifiers -- 5. Colimits -- 6. Exponentials -- 7. Propositional Calculus -- 8. Heyting Algebras -- 9. Quantifiers as Adjoints -- Exercises -- II. Sheaves of Sets -- 1. Sheaves -- 2. Sieves and Sheaves -- 3. Sheaves and Manifolds -- 4. Bundles -- 5. Sheaves and Cross-Sections -- 6. Sheaves as Étale Spaces -- 7. Sheaves with Algebraic Structure -- 8. Sheaves are Typical -- 9. Inverse Image Sheaf -- Exercises -- III. Grothendieck Topologies and Sheaves -- 1. Generalized Neighborhoods -- 2. Grothendieck Topologies -- 3. The Zariski Site -- 4. Sheaves on a Site -- 5. The Associated Sheaf Functor -- 6. First Properties of the Category of Sheaves -- 7. Subobject Classifiers for Sites -- 8. Subsheaves -- 9. Continuous Group Actions -- Exercises -- IV. First Properties of Elementary Topoi -- 1. Definition of a Topos -- 2. The Construction of Exponentials -- 3. Direct Image -- 4. Monads and Beck?s Theorem -- 5. The Construction of Colimits -- 6. Factorization and Images -- 7. The Slice Category as a Topos -- 8. Lattice and Heyting Algebra Objects in a Topos -- 9. The Beck-Chevalley Condition -- 10. Injective Objects -- Exercises -- V. Basic Constructions of Topoi -- 1. Lawvere-Tierney Topologies -- 2. Sheaves -- 3. The Associated Sheaf Functor -- 4. Lawvere-Tierney Subsumes Grothendieck -- 5. Internal Versus External -- 6. Group Actions -- 7. Category Actions -- 8. The Topos of Coalgebras -- 9. The Filter-Quotient Construction -- Exercises -- VI. Topoi and Logic -- 1. The Topos of Sets -- 2. The Cohen Topos -- 3. The Preservation of Cardinal Inequalities -- 4. The Axiom of Choice -- 5. The Mitchell-Bénabou Language -- 6. Kripke-Joyal Semantics -- 7. Sheaf Semantics -- 8. Real Numbers in a Topos -- 9. Brouwer?s Theorem: All Functions are Continuous -- 10. Topos-Theoretic and Set-Theoretic Foundations -- Exercises -- VII. Geometric Morphisms -- 1. Geometric Morphismsand Basic Examples -- 2. Tensor Products -- 3. Group Actions -- 4. Embeddings and Surjections -- 5. Points -- 6. Filtering Functors -- 7. Morphisms into Grothendieck Topoi -- 8. Filtering Functors into a Topos -- 9. Geometric Morphisms as Filtering Functors -- 10. Morphisms Between Sites -- Exercises -- VIII. Classifying Topoi -- 1. Classifying Spaces in Topology -- 2. Torsors -- 3. Classifying Topoi -- 4. The Object Classifier -- 5. The Classifying Topos for Rings -- 6. The Zariski Topos Classifies Local Rings -- 7. Simplicial Sets -- 8. Simplicial Sets Classify Linear Orders -- Exercises -- IX. Localic Topoi -- 1. Locales -- 2. Points and Sober Spaces -- 3. Spaces from Locales -- 4. Embeddings and Surjections of Locales -- 5. Localic Topoi -- 6. Open Geometric Morphisms -- 7. Open Maps of Locales -- 8. Open Maps and Sites -- 9. The Diaconescu Cover and Barr?s Theorem -- 10. The Stone Space of a Complete Boolean Algebra -- 11. Deligne?s Theorem -- Exercises -- X. Geometric Logic and Classifying Topoi -- 1. First-OrderTheories -- 2. Models in Topoi -- 3. Geometric Theories -- 4. Categories of Definable Objects -- 5. Syntactic Sites -- 6. The Classifying Topos of a Geometric Theory -- 7. Universal Models -- Exercises -- Appendix: Sites for Topoi -- Epilogue -- Index of Notation. 330 $aWe dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death. This has cast a shadow on our subsequent work. Our views of topos theory, as presented here, have been shaped by continued study, by conferences, and by many personal contacts with friends and colleagues-including especially O. Bruno, P. Freyd, J.M.E. Hyland, P.T. Johnstone, A. Joyal, A. Kock, F.W. Lawvere, G.E. Reyes, R Solovay, R Swan, RW. Thomason, M. Tierney, and G.C. Wraith. Our presentation combines ideas and results from these people and from many others, but we have not endeavored to specify the various original sources. Moreover, a number of people have assisted in our work by pro­ viding helpful comments on portions of the manuscript. In this respect, we extend our hearty thanks in particular to P. Corazza, K. Edwards, J. Greenlees, G. Janelidze, G. Lewis, and S. Schanuel. 410 0$aUniversitext,$x2191-6675 606 $aGeometry 606 $aK-theory 606 $aLogic, Symbolic and mathematical 606 $aGeometry 606 $aK-Theory 606 $aMathematical Logic and Foundations 615 0$aGeometry. 615 0$aK-theory. 615 0$aLogic, Symbolic and mathematical. 615 14$aGeometry. 615 24$aK-Theory. 615 24$aMathematical Logic and Foundations. 676 $a512/.55 700 $aMac Lane$b Saunders$f1909-2005$4aut$4http://id.loc.gov/vocabulary/relators/aut$026298 702 $aMoerdijk$b Ieke$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962003503321 996 $aSheaves in Geometry and Logic$9382817 997 $aUNINA