TY - JOUR
ID - 2135
TI - Bivariations and tensor products
JO - Iranian Journal of Science
JA - ISTT
LA - en
SN - 2731-8095
AU - Ebrahimi, M. M.
AU - Mahmoudi, M.
AD - Department of Mathematics, Center of Excellence in Algebraic and Logical Structures
in Discrete Mathematics, Shahid Beheshti University, G. C., Tehran, Iran
Y1 - 2011
PY - 2011
VL - 35
IS - 2
SP - 117
EP - 124
KW - Bilinear
KW - bivariance
KW - functional internal lift
KW - tensor product
DO - 10.22099/ijsts.2011.2135
N2 - The ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, Linton and Banaschewski with Nelson defined and studied the tensor product in an equational category and in a general (concrete) category K, respectively, using bimorphisms, that is, defined via the Hom-functor on K. Also, the so-called sesquilinear, or one and a half linear maps and the corresponding tensor products generalize these notions for modules and vector spaces. In this paper, taking a concrete category K and an arbitrary subfunctor H of the functor U¢ = Hom (Uop ´U) rather than just the Hom-functor, where U is the underlying set functor on K, we generalize sesquilinearity to bivariation and study the related notions such as functional internal lifts, universal bivariants, tensor products, and their interdependence.
UR - https://ijsts.shirazu.ac.ir/article_2135.html
L1 - https://ijsts.shirazu.ac.ir/article_2135_a485f282b420d36fbcc29ffa08ca4ba8.pdf
ER -