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Toposes

Elementary toposes

2024.03-04

8 March 2024

Mohamed Barakat
Email: mohamed.barakat@uni-siegen.de
Homepage: https://mohamed-barakat.github.io
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Fabian Zickgraf
Email: fabian.zickgraf@uni-siegen.de
Homepage: https://github.com/zickgraf/
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Mario Román
Email: mromang08@gmail.com
Homepage: https://mroman42.github.io/
Address:
Mathematical Institute
University of Oxford
Oxford, United Kingdom

Tom Kuhmichel
Email: tom.kuhmichel@student.uni-siegen.de
Homepage: https://github.com/TKuh
Address:
Walter-Flex-Str. 3
57068 Siegen
Germany

Contents

1 Toposes
 1.10 Add-methods

  1.10-1 AddCartesianSquareOfSubobjectClassifier

  1.10-2 AddClassifyingMorphismOfSubobject

  1.10-3 AddClassifyingMorphismOfSubobjectWithGivenSubobjectClassifier

  1.10-4 AddCoproductComplement

  1.10-5 AddDirectProductComplement

  1.10-6 AddEmbeddingOfIntersectionSubobject

  1.10-7 AddEmbeddingOfIntersectionSubobjectWithGivenIntersection

  1.10-8 AddEmbeddingOfPseudoComplementSubobject

  1.10-9 AddEmbeddingOfPseudoComplementSubobjectWithGivenPseudoComplement

  1.10-10 AddEmbeddingOfRelativePseudoComplementSubobject

  1.10-11 AddEmbeddingOfRelativePseudoComplementSubobjectWithGivenImplication

  1.10-12 AddEmbeddingOfUnionSubobject

  1.10-13 AddEmbeddingOfUnionSubobjectWithGivenUnion

  1.10-14 AddExactCoverWithGlobalElements

  1.10-15 AddHasPushoutComplement

  1.10-16 AddIndexOfNonliftableMorphismFromDistinguishedObject

  1.10-17 AddInjectionOfCoproductComplement

  1.10-18 AddInjectionOfCoproductComplementWithGivenCoproductComplement

  1.10-19 AddIntersectionSubobject

  1.10-20 AddIsomorphismOntoCartesianSquareOfPowerObject

  1.10-21 AddIsomorphismOntoCartesianSquareOfPowerObjectWithGivenObjects

  1.10-22 AddLawvereTierneyEmbeddingsOfSubobjectClassifiers

  1.10-23 AddLawvereTierneyLocalModalityOperators

  1.10-24 AddLawvereTierneySubobjects

  1.10-25 AddLeftFiberMorphism

  1.10-26 AddLeftFiberMorphismWithGivenObjects

  1.10-27 AddListOfSubobjects

  1.10-28 AddLowerSegmentOfRelation

  1.10-29 AddLowerSegmentOfRelationWithGivenRange

  1.10-30 AddNonliftableMorphismFromDistinguishedObject

  1.10-31 AddPLeftTransposeMorphism

  1.10-32 AddPLeftTransposeMorphismWithGivenRange

  1.10-33 AddPRightTransposeMorphism

  1.10-34 AddPRightTransposeMorphismWithGivenRange

  1.10-35 AddPowerObject

  1.10-36 AddPowerObjectFunctorial

  1.10-37 AddPowerObjectFunctorialWithGivenPowerObjects

  1.10-38 AddPowerObjectLeftEvaluationMorphism

  1.10-39 AddPowerObjectLeftEvaluationMorphismWithGivenObjects

  1.10-40 AddPowerObjectRightEvaluationMorphism

  1.10-41 AddPowerObjectRightEvaluationMorphismWithGivenObjects

  1.10-42 AddProjectionInDirectProductComplement

  1.10-43 AddProjectionInDirectProductComplementWithGivenDirectProductComplement

  1.10-44 AddPseudoComplementSubobject

  1.10-45 AddPushoutComplement

  1.10-46 AddRelativePseudoComplementSubobject

  1.10-47 AddRelativeTruthMorphismOfAnd

  1.10-48 AddRelativeTruthMorphismOfAndWithGivenObjects

  1.10-49 AddRelativeTruthMorphismOfFalse

  1.10-50 AddRelativeTruthMorphismOfFalseWithGivenObjects

  1.10-51 AddRelativeTruthMorphismOfImplies

  1.10-52 AddRelativeTruthMorphismOfImpliesWithGivenObjects

  1.10-53 AddRelativeTruthMorphismOfNot

  1.10-54 AddRelativeTruthMorphismOfNotWithGivenObjects

  1.10-55 AddRelativeTruthMorphismOfOr

  1.10-56 AddRelativeTruthMorphismOfOrWithGivenObjects

  1.10-57 AddRelativeTruthMorphismOfTrue

  1.10-58 AddRelativeTruthMorphismOfTrueWithGivenObjects

  1.10-59 AddRightFiberMorphism

  1.10-60 AddRightFiberMorphismWithGivenObjects

  1.10-61 AddSingletonMorphism

  1.10-62 AddSingletonMorphismWithGivenPowerObject

  1.10-63 AddSubobjectClassifier

  1.10-64 AddSubobjectOfClassifyingMorphism

  1.10-65 AddTruthMorphismOfAnd

  1.10-66 AddTruthMorphismOfAndWithGivenObjects

  1.10-67 AddTruthMorphismOfFalse

  1.10-68 AddTruthMorphismOfFalseWithGivenObjects

  1.10-69 AddTruthMorphismOfImplies

  1.10-70 AddTruthMorphismOfImpliesWithGivenObjects

  1.10-71 AddTruthMorphismOfNot

  1.10-72 AddTruthMorphismOfNotWithGivenObjects

  1.10-73 AddTruthMorphismOfOr

  1.10-74 AddTruthMorphismOfOrWithGivenObjects

  1.10-75 AddTruthMorphismOfTrue

  1.10-76 AddTruthMorphismOfTrueWithGivenObjects

  1.10-77 AddUnionSubobject

  1.10-78 AddUpperSegmentOfRelation

  1.10-79 AddUpperSegmentOfRelationWithGivenRange
2 Category of relations
3 Tools
Index

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