Injectivity in a category: an overview on smallness conditions
Publish Year: 1393
Type: Journal paper
Language: English
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Document National Code:
JR_CGASAT-2-1_006
Index date: 14 September 2021
Injectivity in a category: an overview on smallness conditions abstract
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.
Injectivity in a category: an overview on smallness conditions Keywords:
Injectivity in a category: an overview on smallness conditions authors
M. Mehdi Ebrahimi
Department of Mathematics, Shahid Beheshti University, G.C., Tehran ۱۹۸۳۹, Iran.
Mahdieh Haddadi
Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Mojgan Mahmoudi
Department of Mathematics, Shahid Beheshti University, G.C., Tehran ۱۹۸۳۹, Iran.
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