Ib yam khoom tseem ceeb ntawm cov khub sib txuas yog uas lawv txwv tsis pub sib npaug ntawm cov pawg, thiab qhov no yog qhov peb tau txais hauv Galois txoj kev xav thiab algebraic geometry piv txwv saum toj no: thawj khub sib txuas yog qhov sib npaug los ntawm lub hauv paus theorem ntawm Galois txoj kev xav, thiab ob khub sib txuas txwv tsis pub muaj qhov sib npaug …
Vim li cas cov kab ke sib txuas tseem ceeb?
Cov cuab yeej tseem ceeb tshaj plaws ntawm kev sib txuas yog lawv qhov txuas ntxiv: txhua qhov kev ua haujlwm uas muaj sab laug sab xis (thiab yog li ntawd yog ib qho kev sib txuas sab xis) yog txuas ntxiv (piv txwv li kev mus nrog txwv hauv qeb theoretical kev xav); txhua lub luag haujlwm uas muaj txoj cai adjoint (thiab yog li ntawd yog sab laug adjoint) yog sib txuas (piv txwv li commutes nrog …
Puas yog adjoint functions tshwj xeeb?
Txoj kev sib txuas sab laug lossis sab xis txuas mus rau lub luag haujlwm (Def. 1.1), yog tias muaj, yog qhov tshwj xeeb mus rau ntuj isomorphism. Pov thawj. Piv txwv li tus Functor L:? →? tau muab, thiab peb tab tom thov rau qhov tshwj xeeb ntawm nws txoj cai adjoint, yog tias nws muaj.
Puas yog sab laug adjoint tshwj xeeb?
A sab laug adjoint functionctor muaj a cim txoj cai adjoint mus rau tshwj xeeb natural isomorphism.
hom teeb yog dab tsi?
Nyob rau hauv lej, tshwj xeeb hauv qeb theory, hom-sets, i.e. teeb tsa ntawm morphisms ntawm cov khoom, ua rau muaj qhov tseem ceeb rau pawg ntawm cov khoom. Cov Functors no hu ua hom-functors thiab muaj ntau daim ntawv thov nyob rau hauv qeb txoj kev xav thiab lwm ceg ntawmlej.
