Injectivity in a category: an overview on smallness conditions

سال انتشار: 1393
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 162

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شناسه ملی سند علمی:

JR_CGASAT-2-1_006

تاریخ نمایه سازی: 23 شهریور 1400

چکیده مقاله:

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.

نویسندگان

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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