06629nam 22006255 450 991048032300332120200704114049.01-4612-0927-710.1007/978-1-4612-0927-0(CKB)3400000000089325(SSID)ssj0000808475(PQKBManifestationID)11429842(PQKBTitleCode)TC0000808475(PQKBWorkID)10778289(PQKB)11609920(DE-He213)978-1-4612-0927-0(MiAaPQ)EBC3074007(PPN)237993708(EXLCZ)99340000000008932520121227d1994 u| 0engurnn|008mamaatxtccrSheaves in Geometry and Logic[electronic resource] A First Introduction to Topos Theory /by Saunders MacLane, Ieke Moerdijk1st ed. 1994.New York, NY :Springer New York :Imprint: Springer,1994.1 online resource (XII, 630 p.) Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph0-387-97710-4 Includes bibliographical references and indexes.Prologue -- 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 Morphisms and 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-Order Theories -- 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.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.Universitext,0172-5939GeometryK-theoryMathematical logicGeometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006K-Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11086Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Geometry.K-theory.Mathematical logic.Geometry.K-Theory.Mathematical Logic and Foundations.512/.55MacLane Saundersauthttp://id.loc.gov/vocabulary/relators/aut26298Moerdijk Iekeauthttp://id.loc.gov/vocabulary/relators/autBOOK9910480323003321Sheaves in Geometry and Logic382817UNINA01943nam 2200409 n 450 99639125710331620221107235939.0(CKB)4940000000105124(EEBO)2264220861(UnM)99853894(EXLCZ)99494000000010512419920706d1609 uy |engurbn||||a|bb|A golden keye[electronic resource] opening the locke to eternall happines. Containing seuen most sweete and comfortable directions to a Christian life. By Francis Dillingham, Bachelor in Diuinitie, and Preacher of Gods word at Wilden in Bedfordshire. The contents follow in the next pageLondon Printed [by J. Windet] for Iohn Tapp, and are to be sold at his shop on Tower-hil neare the Bulwarke Gate1609[8], 52, [2] p.; [4], 57; [5], 34 leavesPrinter's name from STC.In two parts; register and pagination separate.Part 2 has separate dated title page, reading: Christian Oeconomy. Or Houshold gouernment."A sermon preached at the solemnization of the funeral of the right vertuous and worshipful Lady Elizabeth Luke" has separate dated title page.Part 2 formerly also STC 6880; identified as STC 6880 on UMI microfilm, reel 579.Reproductions of the original in the Folger Shakespeare Library.Appears at reel 579 #8 (part 1 only) and #9 (part 2 only, identified as STC 6880) (Folger Shakespeare Library copy).eebo-0055Conduct of lifeEarly works to 1800Conduct of lifeDillingham Francisd. 1625.1003764Dillingham Francisd. 1625.autCu-RivESCu-RivESCStRLINWaOLNBOOK996391257103316A golden keye2358589UNISA01840oam 2200541M 450 991071632810332120200213070622.7(CKB)5470000002520857(OCoLC)1065991228(OCoLC)995470000002520857(EXLCZ)99547000000252085720071213d1926 ua 0engurcn|||||||||txtrdacontentcrdamediacrrdacarrierRelief of heirs of Frank Grygla. March 29, 1926. -- Committed to the Committee of the Whole House and ordered to be printed[Washington, D.C.] :[U.S. Government Printing Office],1926.1 online resource (3 pages)House report / 69th Congress, 1st session. House ;no. 707[United States congressional serial set ] ;[serial no. 8536]Batch processed record: Metadata reviewed, not verified. Some fields updated by batch processes.FDLP item number not assigned.ClaimsLegislative amendmentsPer diem allowancesImpeachmentsCivil serviceWagesLegislative materials.lcgftClaims.Legislative amendments.Per diem allowances.Impeachments.Civil service.Wages.Morrow John1865-1935Democrat (NM)1389110WYUWYUOCLCOOCLCQOCLCOOCLCQBOOK9910716328103321Relief of heirs of Frank Grygla. March 29, 1926. -- Committed to the Committee of the Whole House and ordered to be printed3494283UNINA