I came across the notion of inductive limits in C*-algebras, where they exist. Except for the category of finite sets, what are natural examples of categories which fail to have inductive limits?
Categories without inductive limits
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functional-analysis
category-theory
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0Thank you for your comments. – 2012-03-17
1 Answers
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The comments contain the following examples:
- A non-complete Boolean algebra considered as a category;
- The category of Banach/Fréchet/Hilbert spaces with bounded linear maps as morphisms;
- Categories of separable $C^*$-algebras and Banach algebras;
- The category of fields.