The Blueprint Of The Empire State Building
The Blueprint of the Empire State BuildingShilin YuDepartment of MathematicsUniversity of PennsylvaniaMATH 628 Homological AlgebraOct 1, 2014psulogoShilin YuThe Blueprint of the Empire State Building
The Empire State Building in New YorkpsulogoShilin YuThe Blueprint of the Empire State Building
The Empire State Building in Homological Algebrai P0P 0 P 00P F 0i Q0Q0 0F 00F Q00 Q 00 η0iAA0πAAf0A00f 00fB0η00ηiBBπBB00psulogoShilin YuThe Blueprint of the Empire State Building
The Empire State Building made of projective 00 00 iAF100d00d0 0P100F1Q1d0i P0P00···πAη00A00πBf 00B00psulogoShilin YuThe Blueprint of the Empire State Building
Construct the ’beam’ F0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00Want the red square in the middle to be commutive, i.e., η F0 f 0.psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00Check on the subobject P00 P0 , i.e., (η F0 f ) i P00 0.psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00η F0 i P00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0πAAf0η00A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0πAAf0η00A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0πAAf0η00A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 f i A 0 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0πAAf0η00A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 f i A 0 f i P00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 f i A 0 f i P00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 f i A 0 f i P00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P00 P0i P0P000P000P0F00F000F0i Q0Q000 0Q000Q0 00 ηη0iAA0η00πAAf0A00f 00fB0iBBπBB00η F0 i P00 η iQ00 F00 i B η0 F00 i B f 0 0 f i A 0 f i P00 .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000η00πAAf0A00f 00fB0iBBπBB00Claim: f i00P0 η iQ000 F000 factors through i B .psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000η00πAAf0A00f 00fB0iBBπBB00Check: f i00P0 η iQ000 F000 factors through i B , i.e., its composition withπ B is zero.psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000η00πAAf0A00f 00fB0iBBπBB00η iQ000 F000psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000Af0η00πAA00f 00fB0iBBπBB00η iQ000 F000 η00 πQ0 iQ000 F000psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000Af0η00πAA00f 00fB0iBBπBB00η iQ000 F000 η00 πQ0 iQ000 F000 η00 IdQ000 F000 η00 F000psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000Af0η00πAA00f 00fB0iBBπBB00π B f i00P0psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000Af0η00πAA00f 00fB0iBBπBB00π B f i00P0 f 00 π A i00P0psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000πAAf0η00A00f 00fB0iBBπBB00π B f i00P0 f 00 π A i00P0 f 00 00 π P0 πiP000psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000πAAf0η00A00f 00fB0iBBπBB00π B f i00P0 f 00 π A i00P0 f 00 00 π P0 πiP00 f 00 00 Id P000 0f 00 00psulogoShilin YuThe Blueprint of the Empire State Building
Check on the subobject P000 P0i P00i P0P0000P0F00P000F000F0iQ00i Q0Q000 00Q0 00 ηη0iAA0Q000Af0η00πAA00f 00fB0iBBπBB00π B f i00P0 f 00 00 π B η iQ000 F000 η00 F000psulogoShilin YuThe Blueprint of the Empire State Building
Construct higher beams 0Q00η0A0f0B0F0Q0ηAiBfBQ001d00P000F000Q000 00 iAF100d00d0 0P100F1Q1d0i P0P00···πAη00A00πBf 00B00psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00Q0nd0Pn0 1d00λnPn 1Fn0 1Q00nQnλnPn00 1d00Fn00 1d0d00Q0n 1d0λ n 1d0Pn0 2Pn 2λ n 1Fn0 2Q0n 2Q00n 1Qn 1Qn 2Pn00 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn00Fn0Q0nd0d00λnλnPn0 1Pn 1Fn0 1d0γn 1Q0n 1d0Q00nQnPn00 1d00Fn00 1d00Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00d00Q0nd0Pn0 1Pn00 1Pn 1Fn0 1λ n 1d00Q00n 1Qn 1d0Pn0 2λ n 1Pn 2Fn0 2d00Fn00 1d0Q0n 1d0Q00nQnPn00 2γn 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00d00Q0nd0Pn0 1Pn00 1Pn 1Fn0 1d00Fn00 1d0λ n 1Q0n 1d0Q00nQnd00Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00Q0nd0Pn0 1λnd00Pn00 1Pn 1Fn0 1Q00nQnd00Fn00 1d0d00Q0n 1d0Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00Q0nd0Pn0 1λnd00Pn00 1Pn 1Fn0 1Q00nQnd00Fn00 1d0d00Q0n 1d0Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00Q0nd0Pn0 1λnd00Pn00 1Pn 1Fn0 1Q00nQnd00Fn00 1d0d00Q0n 1d0Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn0Fn00d00Q0nd0Pn0 1Pn00 1Pn 1Fn0 1Q00nQnd00Fn00 1d0d00Q0n 1d0d0Pn0 2Q00n 1Qn 1λ n 1Pn 2Fn0 2Q0n 2Qn 2Pn00 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn00Fn0d00Q0nd0Pn0 1Pn00 1Pn 1Fn0 1Q00nQnd00Fn00 1d0d00Q0n 1d0d0Pn0 2Q00n 1Qn 1λ n 1Pn 2Fn0 2Q0n 2Qn 2Pn00 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Construct FnPn0Pn00PnFn00Fn0d00Q0nd0λnPn0 1Pn 1Fn0 1Q00nQnPn00 1d00Fn00 1d0d00Q0n 1d0Q00n 1Qn 1d0Pn0 2Pn00 2Pn 2Fn0 2Q0n 2Qn 2πBd00Fn00 2Q00n 2psulogoShilin YuThe Blueprint of the Empire State Building
Shilin Yu The Blueprint of the Empire State Building. psulogo The Empire State Building in New York Shilin Yu The Blueprint of the Empire State Building. psulogo The Empire State Building in Homological Algebra P0 P P00 Q0 Q Q00 A0 A A00 B0 B B00 i P0 F0 0 00 F00 i Q0 00 i A f0 f
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