Derived functor Homological algebra

-


suppose given covariant left exact functor f : → b between 2 abelian categories , b. if 0 → → b → c → 0 short exact sequence in a, applying f yields exact sequence 0 → f(a) → f(b) → f(c) , 1 ask how continue sequence right form long exact sequence. strictly speaking, question ill-posed, since there numerous different ways continue given exact sequence right. turns out (if nice enough) there 1 canonical way of doing so, given right derived functors of f. every i≥1, there functor rf: → b, , above sequence continues so: 0 → f(a) → f(b) → f(c) → rf(a) → rf(b) → rf(c) → rf(a) → rf(b) → ... . see f exact functor if , if rf = 0; in sense right derived functors of f measure how far f being exact.







Comments

Post a Comment

Popular posts from this blog

CACHEbox ApplianSys

-
cachebox230 server appliance cachebox s caching engine employs code squid project. in 2005 launched becta approved protex content filtering service in collaboration east of england broadband network, represent more 2800 schools across 10 authorities. in 2006, acquired assets , customer base of rival freedom2. has since expanded activity north american schools market , caching device requested schools 2015 e-rate funding.
Read more

Kinship systems Apache

-
hide painting depicting apache girl s puberty ceremony, naiche (chiricahua apache), ca. 1900, oklahoma history center the chiricahua language has 4 different words grandparent: -chú maternal grandmother , -tsúyé maternal grandfather , -chʼiné paternal grandmother , -nálé paternal grandfather . additionally, grandparent s siblings identified same word; thus, 1 s maternal grandmother, 1 s maternal grandmother s sisters, , 1 s maternal grandmother s brothers called -chú. furthermore, grandparent terms reciprocal, is, grandparent use same term refer grandchild in relationship. example, person s maternal grandmother called -chú , maternal grandmother call person -chú (i.e. -chú can mean child of either own daughter or sibling s daughter.) chiricahua cousins not distinguished siblings through kinship terms. thus, same word refer either sibling or cousin (there not separate terms parallel-cousin , cross-cousin). additionally, terms used according sex of speaker (unlike english terms broth...
Read more

Western Apache Apache

-
a western apache woman san carlos group western apache include northern tonto, southern tonto, cibecue, white mountain , san carlos groups. while these subgroups spoke same language , had kinship ties, western apaches considered separate each other, according goodwin. other writers have used term refer non-navajo apachean peoples living west of rio grande (thus failing distinguish chiricahua other apacheans). goodwin s formulation: apache peoples have lived within present boundaries of state of arizona during historic times exception of chiricahua, warm springs, , allied apache, , small band of apaches known apache mansos, lived in vicinity of tucson. cibecue western apache group, according goodwin, north of salt river between tonto , white mountain apache, consisting of ceder creek, carrizo, , cibecue (proper) bands. san carlos. western apache group ranged closest tucson according goodwin. group consisted of apache peaks, arivaipa, pinal, san carlos (proper) bands. arivaipa (also ara...
Read more