Central extensions in semi-abelian categories

✍ Scribed by Dominique Bourn; Marino Gran

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 119 KB
• Volume: 175
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00127-5

✦ Synopsis

In the context of semi-abelian categories, we develop some new aspects of the categorical theory of central extensions by Janelidze and Kelly. If C is a semi-abelian category and X is any admissible subcategory we give several characterizations of trivial and central extensions. The notion of central extension becomes intrinsic when X is the subcategory of the abelian objects in C. We apply these results to the category of internal groupoids in a semi-abelian category. As a very special case, we get the known description of central extensions for crossed modules.