LEADER 01145nam2-2200361---450- 001 990002467820203316 005 20051019153813.0 035 $a000246782 035 $aUSA01000246782 035 $a(ALEPH)000246782USA01 035 $a000246782 100 $a20050907d1987----km-y0itay0103----ba 101 $alat 102 $aBE 105 $aa|||||||001yy 200 1 $aFlorilegia$eFlorilegium Frisingense (CLM 6433), Testimonia divinae scripturae $fedidit Albert Lehner Pubblicazione 210 $aTurnhout$cBrepols$d1987 215 $aXXXIX, 151 p., [2] c. di tav.$cill.$d26 cm 225 2 $aCorpus Christianorum$iSeries Latina$v108 D 410 0$12001$aCorpus Christianorum$iSeries Latina$v108 D 454 1$12001 461 1$1001-------$12001 676 $a878.002 702 1$aLEHNER,$bAlbert 801 0$aIT$bsalbc$gISBD 912 $a990002467820203316 951 $aV.4. Coll.1/ 87 (IV A 864/108 D)$b174769 L.M.$cIV A$d00135031 959 $aBK 969 $aUMA 979 $aVITALE$b90$c20050907$lUSA01$h1655 979 $aCOPAT4$b90$c20051019$lUSA01$h1538 996 $aFlorilegia$9902073 997 $aUNISA LEADER 06629nam 22006255 450 001 9910480323003321 005 20200704114049.0 010 $a1-4612-0927-7 024 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$b[electronic resource] $eA First Introduction to Topos Theory /$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 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-97710-4 320 $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 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. 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. 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Smelser 210 $aBerkeley $cUniversity of California Press$d2013 215 $a1 online resource (150 p.) 225 1 $aThe Clark Kerr lectures on the role of higher education in society 300 $aDescription based upon print version of record. 311 $a0-520-27581-0 320 $aIncludes bibliographical references and index. 327 $aMachine generated contents note: Acknowledgments -- Chapter I: Dynamics of American Universities -- Apologia -- What Kind of Creature is Higher Education? -- Functions -- The Problematic Status of "Functions" -- Moral Embeddedness -- Structural Changes Accompanying Growth -- Increasing the Size of Units -- Segmentation of Units -- Differentiation -- Proliferation -- Coordination -- A Peculiar Case in Higher Education: Structural Accretion -- A Historical Sketch of the Process -- The Discipline-based Academic Department: So Strong and Yet So -- Frail -- The Organized Research Unit as Distraction from Departments -- Reactions and Conflicts Endemic in the Process of Accretion -- Conditions Producing the Endemic Pattern -- Two Long-term Consequences of Accretion -- The Structuring of Faculty Activities -- Implications for Academic Community -- Chapter 2: The Dynamics Ramify: Academic Politics, Conflict, and Inequality -- Instabilities Imposed on Inertial Stability -- Of Pythons and Goats -- Economic Fluctuations -- Competitors for Resources -- Relevance to Accretion -- Accretion and the Growth of Political Constituencies -- Internal Constituencies -- External Constituencies -- Accretion, Revenues, and Costs -- Accretion, Academic Administration, and Higher Education Politics -- Management as Science and Art -- Administration as Threat to Academic Culture -- Administration as Parkinsonian -- The Structural Alternative -- Implications for Shared Governance -- Accretion and Academic Stratification -- Institutional Prestige -- Multicampus Systems and Stratification -- Prestige Among Disciplines -- Chapter 3: Contemporary Trends: Diagnoses and Conditional Predictions -- An Unprecedented Perfect Storm -- Unproductive Paradoxes: Starvation, Accountability, and Governance -- General Consequences of Shifts in Support and Costs -- Accountability, Governance, and Support. -- The Many Faces of Commercialization -- The Language and Imagery of Corporatism and Its -- Consequences -- Consumerism -- Economizing as a Way of Life -- University-Industry Relations -- On-line Distance Instruction and the Rise of the For-profits -- Non-tenured and Part-time Faculty -- Implications for Tenure -- Excursus on Academic Freedom -- Coda -- References. 330 $a"This book is an expanded version of the Clark Kerr Lectures of 2012, delivered by Neil Smelser at the University of California at Berkeley in January and February of that year. The initial exposition is of a theory of change--labeled structural accretion--that has characterized the history of American higher education, mainly (but not exclusively) of universities. The essence of the theory is that institutions of higher education progressively add functions, structures, and constituencies as they grow, but seldom shed them, yielding increasingly complex structures. The first two lectures trace the multiple ramifications of this principle into other arenas, including the essence of complexity in the academic setting, the solidification of academic disciplines and departments, changes in faculty roles and the academic community, the growth of political constituencies, academic administration and governance, and academic stratification by prestige. 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