Formulating Categorical Concepts using Classes

Abstract

We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher categories.

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• Limits of small functors
• Set theory for category theory
• Exact completions and small sheaves
• Well-Pointed Coalgebras