Injectivity in a category: an overview on smallness conditions

نویسندگان

  • M. Mehdi Ebrahimi Department of Mathematics, Shahid Beheshti University, G.C., Tehran 19839, 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 19839, Iran.
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.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

injectivity in a category: an overview on smallness conditions

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 walt...

متن کامل

(r,t)-injectivity in the category $S$-Act

In this paper, we show that injectivity with respect to the class $mathcal{D}$  of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category  well-behaves. Indeed, if $mathcal{M}$ is a subclass of monomorphisms, $mathcal{M}cap mathcal{D}$-injectivity  well-behaves. We also introduce the notion of $(r,t)$-injectivity in the category {bf S-Act}, where $r...

متن کامل

An Overview on Tuberculosis

بیماری سل یک عفونت باکتریایی مزمن است که توسط مایکوباکتریوم توبرکلوزیس ایجاد شده و توسط تشکیل گرانولوما در بافتهای آلوده مشخص می گردد. شایعترین مکان بروز بیماری، ریه ها می باشند. هر چند که سایر ارگانها نیز ممکن است، درگیر بیماری شوند. سل یک بیماری جدید و ناشناخته نیست. این بیماری در گذشته به عنوان کشنده شماره یک در ایالات متحده محسوب می شد و اکنون نیز به عنوان یک عامل مهم مرگ در کل جهان مطرح است.

متن کامل

An overview on genus Thymus

The genus Thymus L. belongs to the Lamiaceae family, consist of about 215 species of herbaceous perennials and small shrubs in the world. They originated from Mediterranean region. This genus is presented in Iranian flora by 14 species, including: T. daenensis, T. carmanicus, T. fallax, T. persicus, T. trautvetteri, T. migricus, T. kotschyanus, T. pubesens, T. nummularius, T. trans...

متن کامل

An Overview on Leishmania Diagnosis

Leishmaniasis is now accounted as a health problem and categorized as a class I disease (emerging and uncontrolled) by World Health Organization (WHO), causing highly significant morbidity and mortality with different clinical presentations. The incidence of human leishmaniasis is increasing and its geographic distribution in humans and animals is shown to be wider than estimated before. Indeed...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 2  شماره 1

صفحات  83- 112

تاریخ انتشار 2014-07-01

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023