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Towards formal Baer criteria
Daniel Misselbeck-Wessel1; Davide Rinaldi
1 Dipartimento di Informatica, Università degli Studi di Verona, Strada le Grazie 15, 37134 Verona, Italy
Confluentes Mathematici, Volume 14 (2022) no. 1, pp. 49-63.

Baer’s criterion helps to identify the injective objects in a category of modules by reducing the problem of map extension to a certain subclass of morphisms. Due to its notorious reliance on Zorn’s lemma, it is inherently non-constructive. However, we put Baer’s criterion on constructive grounds by couching it in point-free terms. Classical principles which will be developed alongside readily allow to gain back the conventional version. Several case studies further indicate a fair applicability.

Received:
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Accepted:
Published online:
DOI: 10.5802/cml.82
Classification: 13C11, 06D22, 03F65
Keywords: Injective module, Baer’s criterion, point-free topology, inductive definition, constructive algebra

Daniel Misselbeck-Wessel 1; Davide Rinaldi 

1 Dipartimento di Informatica, Università degli Studi di Verona, Strada le Grazie 15, 37134 Verona, Italy
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Daniel Misselbeck-Wessel; Davide Rinaldi. Towards formal Baer criteria. Confluentes Mathematici, Volume 14 (2022) no. 1, pp. 49-63. doi : 10.5802/cml.82. https://cml.centre-mersenne.org/articles/10.5802/cml.82/

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