Categories for the Working Mathematician
E157404
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
All labels observed (3)
How this entity was disambiguated
This entity first appeared as the object of triple T1382992 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Categories for the Working Mathematician Context triple: [Saunders Mac Lane, notableWork, Categories for the Working Mathematician]
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A.
Erlangen Program
The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
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B.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
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C.
Memoirs of the American Mathematical Society
Memoirs of the American Mathematical Society is a monograph series featuring long, research-level works in pure and applied mathematics.
-
D.
Annals of Mathematics Studies
Annals of Mathematics Studies is a renowned monograph series in advanced mathematics published by Princeton University Press, featuring influential works across a wide range of mathematical fields.
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E.
Princeton Mathematical Series
Princeton Mathematical Series is a renowned collection of advanced mathematics books published by Princeton University Press, featuring influential works by leading mathematicians.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Categories for the Working Mathematician Target entity description: Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
-
A.
Erlangen Program
The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
-
B.
Grothendieck universe
A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
-
C.
Memoirs of the American Mathematical Society
Memoirs of the American Mathematical Society is a monograph series featuring long, research-level works in pure and applied mathematics.
-
D.
Annals of Mathematics Studies
Annals of Mathematics Studies is a renowned monograph series in advanced mathematics published by Princeton University Press, featuring influential works across a wide range of mathematical fields.
-
E.
Princeton Mathematical Series
Princeton Mathematical Series is a renowned collection of advanced mathematics books published by Princeton University Press, featuring influential works by leading mathematicians.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
category theory textbook
ⓘ
mathematics textbook ⓘ nonfiction book ⓘ |
| author | Saunders Mac Lane ⓘ |
| countryOfPublication |
United States
ⓘ
linked to:
United States of America
|
| field |
category theory
ⓘ
mathematics ⓘ |
| hasChapter |
abelian categories
ⓘ
adjoint functors and limits ⓘ basic concepts of category theory ⓘ monoidal categories and closed categories ⓘ topoi ⓘ universal constructions ⓘ |
| hasConcept |
Kan extensions
ⓘ
Yoneda lemma ⓘ bicompleteness of categories ⓘ enriched categories ⓘ exactness properties in abelian categories ⓘ representable functors ⓘ tensor products of functors ⓘ |
| hasEdition | second edition ⓘ |
| influenced |
algebraic geometry
ⓘ
algebraic topology ⓘ development of modern category theory ⓘ homological algebra ⓘ |
| language | English ⓘ |
| notableFor |
emphasis on applications in working mathematics
ⓘ
rigorous axiomatic approach ⓘ systematic development of category theory ⓘ |
| originalPublicationYear | 1971 ⓘ |
| pageCountApproximate | 300 ⓘ |
| publisher |
Springer-Verlag
ⓘ
linked to:
Springer
|
| secondEditionPublicationYear | 1998 ⓘ |
| series | Graduate Texts in Mathematics ⓘ |
| subject |
abelian categories
ⓘ
adjoint functors ⓘ categories ⓘ functors ⓘ limits and colimits ⓘ monads ⓘ monoidal categories ⓘ natural transformations ⓘ topoi ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
professional mathematicians ⓘ |
| usedAs |
graduate-level textbook
ⓘ
standard reference in category theory ⓘ |
| volumeNumber | 5 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Categories for the Working Mathematician Description of subject: Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Saunders
linked to: Categories for the Working Mathematician
Freyd adjoint functor theorem
→
standardReference
→
Saunders Mac Lane – Categories for the Working Mathematician
ⓘ
linked to: Categories for the Working Mathematician