Baer criterion in locally presentable categories

Document Type : Research Paper

Authors

1 Mojgan Mahmoudi; Professor Department of Mathematics, Shahid Beheshti University,

2 Faculty of Mathematical Sciences, Department of Mathematics, Shahid Beheshti University, 19839 Tehran, Iran.

10.48308/cgasa.2024.235938.1495

Abstract

In this paper, some Baer type criteria are considered for locally presentable categories. Recalling the notion of the classical Baer criterion for injectivity, it is shown that a locally presentable category which has enough injectives and coproduct injections, which are monomorphisms, satisfy such criterion if and only if the class of its injective objects is accessibly embedded in the category. Also, it is shown that this criterion is equivalent to the Baer type criterion that injectivity is equivalent to injectivity with respect to a subclass of monomorphisms.

It is also proved some Baer type criteria for $\lambda$-presentable categories for injectivity with respect to monomorphisms with $\lambda$-presentable domains and codomains, for a regular cardinal number $\lambda$.
In particular, some Baer type criteria is found for varieties.

Keywords

Main Subjects

References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 19 July 2024

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