本质小范畴相关定义的合适文献引用请求
本质小范畴相关定义的合适文献引用请求
Hey there! Since you're new to category theory and hunting for solid citations to back up that nLab statement about essentially small categories, here are some trusted options you can use:
- Saunders Mac Lane's Categories for the Working Mathematician: This is the classic "go-to" textbook for category theory. It clearly lays out the definition of essentially small categories, along with the equivalent characterizations (like being equivalent to a small category, having a small skeleton when assuming the axiom of choice, and the link to locally small categories with a small number of object isomorphism classes). It's super authoritative and widely recognized in the field.
- Francis Borceux's Handbook of Categorical Algebra (Volume 1): If you need more detailed, rigorous coverage, this handbook is perfect. The first volume dedicates sections to category size concepts, including all the equivalent conditions for a category to be essentially small—great for more formal academic writing.
- Tom Leinster's Basic Category Theory: For a more modern, accessible take, this textbook covers the key definitions and equivalences around essentially small categories in a clear, approachable way. It's a good pick if your audience includes newer learners of category theory.
As a side note: If your academic context accepts online scholarly resources, the nLab entry itself is also a valid citation—it's curated and reviewed by the category theory community, so its content is well-vetted.
备注:内容来源于stack exchange,提问作者max_121
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