2/4 Introduction to Grothendieck toposes
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| Part Number | 2 | |
| Number of Parts | 4 | |
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/36340 (DOI) | |
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00:00
TopostheorieAbelian categoryEvent horizonArrow of timeStability theoryAxiomPressureCodomainSheaf (mathematics)Phase transitionSheaf (mathematics)Sieve of EratosthenesPosition operatorPhysical lawCondition numberDivisorObject (grammar)Category of beingArrow of timeFamilyRight angleComputer animation
01:01
Abelian categoryTopostheorieFunction (mathematics)AxiomStability theoryArrow of timeSample (statistics)Ideal (ethics)AlgebraBasis <Mathematik>Element (mathematics)Free productSheaf (mathematics)FamilyCondition numberSet theorySheaf (mathematics)Spherical capCategory of beingWeightMusical ensembleObject (grammar)Maxima and minimaSieve of EratosthenesNetwork topologyTopologischer RaumOpen setStability theoryNatural numberStandard errorSign (mathematics)AreaGroup actionMassComputer animation
02:46
Abelian categoryArrow of timeCodomainTopostheorieTopologySheaf (mathematics)Inclusion mapCondition numberFamilyObject (grammar)Open setSieve of EratosthenesSpacetimePhysical lawNetwork topologyStability theoryDistributive propertyOrder (biology)Arrow of timeAxiomCategory of beingSet theoryDistribution (mathematics)InfinityTopologischer RaumCircleGraph coloringPhase transitionNatural numberMultiplication signObservational studyResultantMatching (graph theory)Saddle pointComputer animationLecture/Conference
06:07
TopostheorieFunction (mathematics)Abelian categoryAxiomStability theoryArrow of timeNetwork topologyCovering spaceSieve of EratosthenesMoment (mathematics)Stability theoryAxiomSlide ruleCondition numberCategory of beingReflexive relationGrothendieck topologyFunctional (mathematics)Maxima and minimaGroup actionMany-sorted logicSet theoryArrow of timeSheaf (mathematics)Physical lawAverageRoutingOrder (biology)Observational studyComputer animation
08:18
Abelian categoryTopostheorieSquare numberSample (statistics)Arrow of timeCodomainTheoryPerspective (visual)Population density1 (number)Condition numberNetwork topologyAxiomRight angleGrothendieck topologyCovering spaceCategory of beingObject (grammar)Fiber bundleSieve of EratosthenesRule of inferenceMaß <Mathematik>Hand fanSeries (mathematics)Moving averageMusical ensembleConfidence intervalMereologyCausalityStandard errorCircleMultiplication signMany-sorted logicAreaComputer animation
10:38
TopologyAbelian categoryIdeal (ethics)Ring (mathematics)Canonical ensembleAlgebraBasis <Mathematik>TopostheorieSample (statistics)Category of beingCanonical ensembleTheoryNetwork topologyGroup representationAlgebraic structureSpacetimeTopostheorieTopologischer RaumLattice (group)Natural numberPoint (geometry)Multiplication signFamilyLogicGraph coloringGroup actionComputer animation
11:51
TopologyAbelian categoryIdeal (ethics)Limit (category theory)Element (mathematics)AlgebraBasis <Mathematik>Ring (mathematics)TopostheorieSample (statistics)Point (geometry)FinitismusLimit (category theory)Lattice (group)Open setInfinityDistributive propertyGrothendieck topologyCategory of beingEnergy levelCanonical ensembleElement (mathematics)Stability theoryFamilyNetwork topologyCondition numberEvent horizonLecture/ConferenceComputer animation
12:42
TopologyAbelian categoryIdeal (ethics)Element (mathematics)AlgebraBasis <Mathematik>Ring (mathematics)TopostheorieSample (statistics)AlgebraOpen setTopologischer RaumObject (grammar)Observational studyNetwork topologyCategory of beingGroup actionEvent horizonWave packetNumerical analysisConstraint (mathematics)Element (mathematics)Positional notationPropositional calculusLogicJunction (traffic)Standard errorLecture/ConferenceComputer animation
14:20
TopologyAbelian categoryBoom barrierIdeal (ethics)Limit (category theory)Ring (mathematics)AlgebraBasis <Mathematik>TopostheorieSample (statistics)Many-sorted logicAreaHand fanConnected spaceSpacetimeKörper <Algebra>Nominal numberForcing (mathematics)Inequality (mathematics)Group actionGrothendieck topologyChemical equationArithmetic meanFundamental theorem of algebraGame theoryCuboidCategory of beingMaß <Mathematik>Degrees of freedom (physics and chemistry)FamilyModulformModel theoryOrder (biology)FinitismusObject (grammar)MathematicsShift operatorLinear subspaceInvariant (mathematics)Open setRing (mathematics)Einbettung <Mathematik>Trigonometric functionsCovering spaceCanonical ensembleElement (mathematics)Network topologyDuality (mathematics)Arrow of timeFormal power seriesPositional notationIdeal (ethics)Local ringTopostheorieAlgebraFree groupPoint (geometry)GeometryLimit (category theory)ConsistencyDegree (graph theory)Lattice (group)Topologischer RaumBasis <Mathematik>Computer animation
19:16
Abelian categoryFunktorFunction (mathematics)Element (mathematics)Free productTopostheorieElement (mathematics)Category of beingSet theoryArrow of timeSieve of EratosthenesPrice indexCondition numberDivisorFamilyCircleStandard errorComputer animation
20:14
ResultantEvent horizonStandard errorStress (mechanics)GoogolWeightAmalgam (chemistry)Arrow of timeCondition numberSieve of EratosthenesEqualiser (mathematics)Right angleElement (mathematics)Category of beingTheory of relativityFamilyMaß <Mathematik>Lecture/Conference
22:39
TopostheorieElement (mathematics)Function (mathematics)Free productSheaf (mathematics)Abelian categoryUniqueness quantificationAmalgam (chemistry)FamilySet theoryMaß <Mathematik>Arrow of timePrice indexElement (mathematics)Shift operatorCategory of beingOperator (mathematics)Grothendieck topologyDuality (mathematics)ComputabilityNegative numberLimit (category theory)Algebraic structureTopostheoriePoint (geometry)SpacetimeTopologischer RaumPresentation of a groupMathematicsEquivalence relationMorley's categoricity theoremModulformClassical physicsNetwork topologyObservational studyExistenceInvariant (mathematics)Different (Kate Ryan album)Matching (graph theory)Covering spaceResultantLogicPhase transitionMetreNumerical analysisArchaeological field surveyEvent horizonState of matterOrder (biology)Prisoner's dilemmaCuboidGraph coloringCausalityComputer animationLecture/Conference
28:02
Abelian categoryTopologyGroup actionSet theoryTopostheorieSample (statistics)Category of beingPoint (geometry)TopostheorieTerm (mathematics)Topologischer RaumLimit (category theory)Category of beingExtension (kinesiology)Complete metric spaceSpacetimeFinitismusObject (grammar)Operator (mathematics)Open setIdempotentNetwork topologyNatural numberAlgebraic closureSet theoryFundamental theorem of algebraMathematicsCompact spaceRepresentation theoryFree group1 (number)4 (number)Sign (mathematics)Combinatory logicOrder (biology)SummierbarkeitArchaeological field surveySpecial unitary groupState of matterForcing (mathematics)AreaWave packetMilitary baseGroup actionGraph coloringJunction (traffic)Computer animation
32:53
Mortality rateSet theoryLocal ringTopostheorieEquivalence relationNetwork topologyCorrespondence (mathematics)Lecture/Conference
33:44
Abelian categoryTopologySet theoryGroup actionTopostheorieSample (statistics)Category of beingTopologische GruppeGroup actionAnalytic continuationGrothendieck topologyTopostheorieCategory of beingSet theoryRoutingGraph coloringInequality (mathematics)Network topologyComputer animationLecture/Conference
34:47
Abelian categoryTopologyGroup actionSet theoryTopostheorieSample (statistics)Category of beingObservational studyMathematical modelUniqueness quantificationCategory of beingSet theoryArithmetic meanEquivalence relationFiber bundleTopostheorieTopologische GruppeTheory of relativityComputer animation
35:34
Abelian categoryObject (grammar)Inclusion mapTopostheorieSet theoryLimit (category theory)FunktorPresentation of a groupSheaf (mathematics)Algebraic structureCondition numberInclusion mapCategory of beingRadical (chemistry)Limit (category theory)FunktorApproximationObject (grammar)Morley's categoricity theoremEnergy levelDiagramSet theoryTerm (mathematics)ResultantEvent horizonMaß <Mathematik>Order (biology)RoutingComputer animation
37:20
Sheaf (mathematics)Potenz <Mathematik>ExistenceCategory of beingFunktorObject (grammar)ResultantVotingParameter (computer programming)Order (biology)Lecture/Conference
38:16
Abelian categoryObject (grammar)Inclusion mapTopostheorieSet theoryFunktorExistenceCategory of beingObject (grammar)Sheaf (mathematics)Potenz <Mathematik>Lemma (mathematics)Universe (mathematics)Correspondence (mathematics)Arrow of timeAntimatterGoogolFlow separationRule of inferenceComputer animationLecture/Conference
39:36
Abelian categoryObject (grammar)Inclusion mapTopostheorieSet theoryFunktorCategory of beingSet theorySheaf (mathematics)Generating set of a groupObject (grammar)Musical ensembleCanonical ensembleFunktorArrow of timeTopostheorieMaß <Mathematik>Einbettung <Mathematik>Grothendieck topologyPresentation of a groupTopologischer RaumAxiom of choiceModulformSocial classSpacetimeMilitary baseNetwork topologyMultiplication signBasis <Mathematik>DivisorRule of inferenceGraph coloringBounded variationSpecial unitary groupCollisionState of matterComputer animationLecture/Conference
44:03
Abelian categoryObject (grammar)TopostheorieSet theoryFunktorLimit (category theory)Grothendieck topologyDifferent (Kate Ryan album)TopostheorieSpacetimeMilitary baseCategory of beingNetwork topologyMorphismusDuality (mathematics)Topologischer RaumFundamental theorem of algebraBasis <Mathematik>Event horizonPhysical lawComputer animation
45:08
TopostheorieTransformation (genetics)GeometryAbelian categoryDirected setLimit (category theory)Fiber (mathematics)MorphismusPoint (geometry)Continuous functionAreaTopologischer RaumEnergy levelFunktorMorphismusTopostheorieSpacetimePhysical lawRight angleFilm editingEvent horizonObservational studyAdditionComputer animationLecture/Conference
46:01
TopostheorieTransformation (genetics)Abelian categoryDirected setLimit (category theory)Fiber (mathematics)MorphismusPoint (geometry)Transformation (genetics)MorphismusSet theoryRight angleGoodness of fitInverse elementTopologischer RaumTopostheorieFinitismusCategory of beingLimit (category theory)Point (geometry)FunktorGeometryContinuous functionGroup actionEvent horizonAnalytic continuationComputer animation
46:55
TopologyFunction (mathematics)TopostheorieUniqueness quantificationFunktorMorphismusDirected setSubsetFiber (mathematics)Sheaf (mathematics)Inclusion mapSample (statistics)Exact sequenceFiber bundleGroup actionWell-formed formulaOpen setFunktorContinuous functionDirection (geometry)MathematicsInverse elementShift operatorSpacetimeCorrespondence (mathematics)MorphismusFiber bundleHomomorphismusComputer animationLecture/Conference
47:52
SpacetimeFamilyTerm (mathematics)Algebraic structureSet theoryGame theoryTopostheorieContinuous functionOperator (mathematics)FunktorInverse elementLimit (category theory)Shift operatorFiber bundleLecture/Conference
48:58
TopologyFunction (mathematics)TopostheorieUniqueness quantificationFunktorMorphismusDirected setSubsetFiber (mathematics)Fiber bundleSheaf (mathematics)Inclusion mapSample (statistics)Exact sequenceSet theoryRadical (chemistry)Element (mathematics)TopostheorieSheaf (mathematics)Shift operatorObject (grammar)Arrow of timeMorphismusInclusion mapFunktorLimit (category theory)Fundamental theorem of algebraResultantSocial classGeometryGoodness of fitEvent horizonStandard errorOrder (biology)Decimal1 (number)Computer animation
50:09
FunktorAbelian categoryCurvatureTopostheorieLimit (category theory)TheoremPoint (geometry)Shift operatorTopostheorieModel theoryPhysical lawLocal ringMorphismusDescriptive statisticsBuildingDivisorComputer animationLecture/Conference
51:17
Abelian categoryFunktorCurvatureTopostheorieLimit (category theory)TheoremPoint (geometry)Event horizonProduct (business)Wage labourFunktorCategory of beingMany-sorted logicDiagramMultikollinearitätTopostheorieIsomorphieklasseTensorproduktComputer animation
52:03
Archaeological field surveySpecial unitary groupDivision (mathematics)Quadratic formPresentation of a groupJunction (traffic)FamilyTrailEvent horizonTopostheorieFree groupGroup representationTerm (mathematics)MultikollinearitätComplete metric spaceEinbettung <Mathematik>FunktorDirection (geometry)Limit (category theory)Point (geometry)Category of beingLecture/Conference
53:42
FunktorAbelian categoryTopostheorieCurvatureLimit (category theory)TheoremPoint (geometry)MorphismusEinbettung <Mathematik>FunktorCurvatureFinitismusLimit (category theory)Category of beingInsertion lossCausalityHand fanGroup representationTopostheorieDescriptive statistics1 (number)FamilyShift operatorDivisorCondition numberAnalytic continuationEvent horizonCircleCohesion (computer science)Computer animationLecture/Conference
54:40
Inclusion mapEinbettung <Mathematik>Fiber (mathematics)GeometryTheoremTopostheorieProof theoryCategory of beingArrow of timeFunktorTime domainCurvatureCanonical ensembleElement (mathematics)FunktorEquivalence relationAnalytic continuationConnected spaceAreaCartesian coordinate systemTopostheorieGroup actionWeightElement (mathematics)Set theoryCategory of beingLimit (category theory)Condition numberTheoryCurvatureFamilyEvent horizonAngleStandard errorComputer animationLecture/Conference
56:52
MorphismusTopostheorieCanonical ensembleInfinityLimit (category theory)TheoremInsertion lossFamilyCircleNichtlineares GleichungssystemGraph coloringObject (grammar)Lattice (order)Food energyCategory of beingMereologyBasis <Mathematik>Condition numberCodomainMorphismusTopostheorieLimit (category theory)Grothendieck topologyFunktorPopulation densityComplete metric spaceSocial classDuality (mathematics)Many-sorted logicResultantCartesian coordinate systemDirection (geometry)TheoryComputer animation
59:46
Multiplication signTopologischer RaumDirection (geometry)TopostheorieUniverse (mathematics)Open setLimit (category theory)Set theoryNetwork topologyContinuous functionMathematicsGrothendieck topologyLecture/Conference
Transcript: English(auto-generated)