Strongly FP-injective and strongly flat functors
L Mao - Rendiconti del Seminario Matematico della Università …, 2016 - numdam.org
L Mao
Rendiconti del Seminario Matematico della Università di Padova, 2016•numdam.orgGiven a ring R, denote by mod-R the category of nitely presented right R-modules, the two
functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of
abelian groups have received extensive attention since the s. Particularly they play
important roles in the investigation of the model theory of modules and the representation
theory of Artinian algebras (see eg [,,,,,,,,,,]). Strikingly, Herzog has developed a general
theory for the category (mod-R, Ab) and ((mod-R) op, Ab) for any ring R (see [,]). It is well …
functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of
abelian groups have received extensive attention since the s. Particularly they play
important roles in the investigation of the model theory of modules and the representation
theory of Artinian algebras (see eg [,,,,,,,,,,]). Strikingly, Herzog has developed a general
theory for the category (mod-R, Ab) and ((mod-R) op, Ab) for any ring R (see [,]). It is well …
Given a ring R, denote by mod-R the category of nitely presented right R-modules, the two functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of abelian groups have received extensive attention since the s. Particularly they play important roles in the investigation of the model theory of modules and the representation theory of Artinian algebras (see eg [,,,,,,,,,,]). Strikingly, Herzog has developed a general theory for the category (mod-R, Ab) and ((mod-R) op, Ab) for any ring R (see [,]).
It is well known that both (mod-R, Ab) and ((mod-R) op, Ab) are locally nitely presented Grothendieck additive categories. There is a full and faithful right exact functor from the category R-Mod of left R-modules to (mod-R, Ab), which is given by the rule M! M. Similarly, the functor given by M!.; M/from
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