“Abelian Categories: An Introduction to the Theory of Functors”
E621117
“Abelian Categories: An Introduction to the Theory of Functors” is a foundational monograph in category theory that systematically develops the theory of abelian categories and functors, significantly shaping modern homological algebra.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “Abelian Categories: An Introduction to the Theory of Functors” canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T6834108 — 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: “Abelian Categories: An Introduction to the Theory of Functors” Context triple: [Peter Freyd, notableWork, “Abelian Categories: An Introduction to the Theory of Functors”]
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A.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
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B.
Grothendieck category
A Grothendieck category is an abelian category with exact filtered colimits and a generator, providing a highly general framework that extends the properties of module and sheaf categories in homological algebra.
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C.
Sheaves in Geometry and Logic
Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
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D.
Grothendieck spectral sequence
The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
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E.
Grothendieck duality
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
- 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: “Abelian Categories: An Introduction to the Theory of Functors” Target entity description: “Abelian Categories: An Introduction to the Theory of Functors” is a foundational monograph in category theory that systematically develops the theory of abelian categories and functors, significantly shaping modern homological algebra.
-
A.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
-
B.
Grothendieck category
A Grothendieck category is an abelian category with exact filtered colimits and a generator, providing a highly general framework that extends the properties of module and sheaf categories in homological algebra.
-
C.
Sheaves in Geometry and Logic
Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
-
D.
Grothendieck spectral sequence
The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
-
E.
Grothendieck duality
Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| aimsTo |
clarify the role of functors in homological algebra
ⓘ
provide a systematic treatment of abelian categories ⓘ |
| contribution |
systematic development of the theory of abelian categories
ⓘ
systematic development of the theory of functors ⓘ |
| describedAs | foundational monograph in category theory ⓘ |
| field |
category theory
ⓘ
homological algebra ⓘ |
| focusesOn |
categorical foundations of homological algebra
ⓘ
functorial methods in algebra ⓘ structure and properties of abelian categories ⓘ |
| genre | mathematics literature ⓘ |
| hasForm | monograph ⓘ |
| hasTheoreticalImportance | high ⓘ |
| hasTopic |
additive functors
ⓘ
categorical formulation of homological algebra ⓘ derived functors and cohomology ⓘ diagram chasing in abelian categories ⓘ exact functors and left/right exactness ⓘ exact sequences in abelian categories ⓘ kernels and cokernels in abelian categories ⓘ |
| influenceOn | modern homological algebra ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in category theory ⓘ researchers in homological algebra ⓘ |
| isUsedFor |
advanced courses in category theory
ⓘ
advanced courses in homological algebra ⓘ foundations of derived functors ⓘ study of abelian categories ⓘ study of functorial constructions ⓘ |
| language | English ⓘ |
| mainSubject |
abelian categories
ⓘ
derived functors ⓘ exact functors ⓘ functors ⓘ homological algebra ⓘ |
| recognizedAs |
important reference in category theory
ⓘ
important reference in homological algebra ⓘ |
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: “Abelian Categories: An Introduction to the Theory of Functors” Description of subject: “Abelian Categories: An Introduction to the Theory of Functors” is a foundational monograph in category theory that systematically develops the theory of abelian categories and functors, significantly shaping modern homological algebra.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.