toposes, triples and theories - m. barr, w. wells

《toposes, triples and theories - m. barr, w. wells》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MichaelBarrCharlesWellsToposes,TriplesandTheoriesVersion1.110September2000Copyright2000byMichaelBarrandCharlesFrederickWells.Thisversionmaybedownloadedandprintedinunmodiedformforprivateuseonly.Itisavailableathttp://www.cwru.edu/artsci/math/wells/pub/ttt.htmlandf

2、tp.math.mcgill.ca/pub/barrasanyofthelesttt.dvi,ttt.ps,ttt.ps.zip,ttt.pdf,ttt.pdf.zip.MichaelBarrPeterRedpathProfessorEmeritusofMathematics,McGillUniversitybarr@barrs.orgCharlesWellsProfessorEmeritusofMathematics,CaseWesternReserveUniversityAliateScholar,Oberlin

3、Collegecharles@freude.comToMarciaandJaneContentsPrefacevi1.Categories11.1Denitionofcategory11.2Functors111.3Naturaltransformations161.4ElementsandSubobjects201.5TheYonedaLemma261.6Pullbacks291.7Limits351.8Colimits481.9Adjointfunctors541.10Filteredcolimits671.11N

4、otestoChapterI712.Toposes742.1BasicIdeasaboutToposes742.2SheavesonaSpace782.3PropertiesofToposes862.4TheBeckConditions922.5NotestoChapter2953.Triples973.1DenitionandExamples973.2TheKleisliandEilenberg-MooreCategories1033.3Tripleability1093.4PropertiesofTripleabl

5、eFunctors1223.5SucientConditionsforTripleability1283.6MorphismsofTriples1303.7AdjointTriples1353.8HistoricalNotesonTriples1424.Theories1444.1Sketches1454.2TheEhresmann-KennisonTheorem1494.3Finite-ProductTheories1524.4LeftExactTheories1584.5NotesonTheories170iv5.

6、PropertiesofToposes1735.1TripleabilityofP1735.2SlicesofToposes1755.3LogicalFunctors1785.4ToposesareCartesianClosed1835.5ExactnessPropertiesofToposes1865.6TheHeytingAlgebraStructureon1936.PermanencePropertiesofToposes1986.1Topologies1986.2SheavesforaTopology2036.3

7、Sheavesformatopos2096.4Leftexactcotriples2116.5Leftexacttriples2156.6CategoriesinaTopos2206.7GrothendieckTopologies2266.8Giraud'sTheorem2317.RepresentationTheorems2407.1Freyd'sRepresentationTheorems2407.2TheAxiomofChoice2457.3MorphismsofSites2497.4Deligne'sTheore

8、m2567.5NaturalNumberObjects2577.6CountableToposesandSeparableToposes2657.7Barr'sTheorem2727.8NotestoChapter72748.CoconeTheories2778.1RegularTheories2778.2Finit