
hyperhomology

samaroop bijganitemadhye, hyperhomology kinwa hypercolomology (sootra 1) heey (saha) samarupata functorche samanyikaran aahe jeey abelian shreni sootra _ 2 madheel vastoo mhanoon navhe tarr vastoonchya sakhali sankulanmadhye input mhanoon ghetat, mhanoon sootra _ 3 madheel vastoo. heey ekhadya vastuche vyutpann functor samarupata aanee sakhali sankulachya samarupata yanchyatil eka prakarche cross aahe kaaran hypercolomology vyutpann jaagtik vibhaganchya functor sootra _ 4 shhee sambandhit aahe. 
hyperhomologycha aata farsa vapar hott naheeh sumare 1970 pasoon tyachi jaaga mothya pramanat vyutpann shreninmadhil vyutpann functorchya andaje samatulya sankalpnene ghetali aahe.
prerana.
hypercolomologychi eka prerana yaa vastusthitivarun yete qee formula _ 5i yaa sankshipt achook anukramanshi sambandhit samarupavadi dirgh achook anukramanche spasht samanyikaran nahee.eae. eka sambandhit lamb achook anukram formula _ 6 aahe, heey asey disun yete qee hypercolomology aniyantrit lamb achook anukram formula _ 7 pasoon samaan samaroop sambandhit lamb achook kram tayar karnyasathi tantre dete kaaran tyache input keval abelian shrenitil vastunaivaji sakhali sankulandware dile jaatat. aapan yaa sakhali sankulache eka vishisht trikonat rupantar karoo shakato (vyutpann shrenivaril trikonatmak shreninchi bhasha vaparoon) sootra _ 8, jeey aapan biformula _ 9 darshavito, tyanantar vyutpann jaagtik vibhag sootra _ 4 ghetalyane eka lamb achook kram midato, joou hypercolomology gatancha eka lamb achook kram aahe.
vyakhya.
heey adhik samanya asalyane aamhi hypercolomologychi vyakhya deto. nehmipramane, hypercohology aanee hyperhomology moolatah samaan aaheth eka duherikaran karoon ekapasoon dusyakday rupantarit hote, i.eae. serve bananchi disha badaloon, injectionchya vastoonchya jaagi projective bananchi jaaga gheuun, ityadi. 
samaja qee "aaa" hii puresha injections asaleli abelian shreni aahe aanee "eff" hii dusya abelian shreni "buub" sathee davikadil achook functor aahe. 
jarr 'see' haah davikade bandhalelya 'aii' chya vastooncha samooh asel, tarr hypercolomology 
see" chaa (purnank "aay" sathee) aahe
khalilpramane ganana keleeh
see" chey atee madyavidnyan heey adviteey samarupateparyant, ardh-samarupatechya nivadipasoon swatantra aahe. 
vyutpann shreni vaparoon hypercolomologychi vyakhya dekhil kelee jaau shakateh 'see' chey hypercolomology heey fakt 'rf' ('see') chey cohomology aahe jeey 'bii' chya vyutpann shrenicha ghatak manale jaate.
nakaratmak nirdeshankansathi nahisha honanya sankulansathi, hypercolomologychi vyakhya etch0 = "fh" 0 = "etch" 0 "eff" chey vyutpann ghatak mhanoon kelee jaau shakate.
hyper alcohology varnakrameey anukram.
done hypercolomology varnakrameey anukram aahet; eka 'eae' 2 sandnyesah 
aanee dusari 'eae' 1 sandnyesah 
aanee 'eae' 2 sandnya 
donhi hypercolomologymadhye rupantarit hott aahet 
jethe "r" "j" "f" haah "f" chaa yogya vyutpann functor aahe.
anuprayog.
hyper alcohology varnakrameey anukramancha eka vapar jarbchya abhyasat aahe. lakshat thewa qee avkash sootra _ 15 vareel rank aine vector bundleche vargikaran sech-alcohology gut sootra _ 16 mhanoon kele jaau shakate. jerbsmagil mukhya kalpana hii kalpana samarupatene vadhavane aahe, mhanoon kahee functor sootra _ 18 sathee sootra _ 17 ghenyaivaji, aapan tyaeivaji samarupata gut sootra _ 19 chaa vichar karato, mhanoon teey mool vargikaran gatatil vastundvare chikatalelya vastunche vargikaran karate. deligney-alcohology haah eka jawalcha sambandhit vishay aahe joou jerb aanee hypercolomologycha abhyas karato.