TY - JOUR
ID - 6800
TI - Injectivity in a category: an overview on smallness conditions
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Ebrahimi, M. Mehdi
AU - Haddadi, Mahdieh
AU - Mahmoudi, Mojgan
AD - Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, Iran.
AD - Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Y1 - 2014
PY - 2014
VL - 2
IS - 1
SP - 83
EP - 112
KW - Cogenerating set
KW - essential extension
KW - residual smallness
KW - injective
DO -
N2 - Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and Walter Tholen, who studied these notions in a much more categorical setting. Then, we study these notions as well as the well behavior of injectivity, in the class $mod(Sigma, {mathcal E})$ of models of a set $Sigma$ of equations in a suitable category, say a Grothendieck topos ${mathcal E}$, given by M.Mehdi Ebrahimi. We close the paper by some examples to support the results.
UR - http://cgasa.sbu.ac.ir/article_6800.html
L1 - http://cgasa.sbu.ac.ir/article_6800_3a21602701c668271925317f72f7ea0a.pdf
ER -