Abstract
The notions of a locally α-presentable and locally α-generated categories are introduced, where α is a regular cardinal. The properties of these categories are studied extensively, in particular their close relationship with other types of categories. Also the subclasses of topos, algebraic categories and locally α-noetherian categories are investigated in detail. A “classification” of locally α-presentable, locally α-generated categories, locally α-noetherian categories and algebraic categories is given.
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This note is a summary of a joint paper with P. Gabriel. It is an outgrowth of mostly unpublished papers and manuscripts of both authors from 1965–69, cf. [8], [20], [21], [22]. Details will appear elsewhere.
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Ulmer, F. (1971). Locally α-presentable and locally α-generated categories. In: Gray, J.W. (eds) Reports of the Midwest Category Seminar V. Lecture Notes in Mathematics, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072314
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DOI: https://doi.org/10.1007/BFb0072314
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