Freyd–Kelly factorization system
E621115
The Freyd–Kelly factorization system is a concept in category theory that generalizes the idea of factoring morphisms into two classes with specific lifting and composition properties, providing a unifying framework for many standard factorization results.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Freyd–Kelly factorization system canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6834097 — 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: Freyd–Kelly factorization system Context triple: [Peter Freyd, notableWork, Freyd–Kelly factorization system]
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A.
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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B.
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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C.
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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D.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
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E.
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.
- 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: Freyd–Kelly factorization system Target entity description: The Freyd–Kelly factorization system is a concept in category theory that generalizes the idea of factoring morphisms into two classes with specific lifting and composition properties, providing a unifying framework for many standard factorization results.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
E.
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.
- F. None of above. chosen
Statements (29)
| Predicate | Object |
|---|---|
| instanceOf |
categorical concept
ⓘ
factorization system ⓘ structure in category theory ⓘ |
| appliesTo | morphisms in a category ⓘ |
| assumes | a given category as ambient context ⓘ |
| context |
abstract homotopy theory
ⓘ
higher category theory ⓘ |
| describes | factorization of morphisms ⓘ |
| field | category theory ⓘ |
| generalizes |
classical factorization systems in categories
ⓘ
orthogonal factorization systems ⓘ |
| hasComponent |
left class of morphisms
ⓘ
right class of morphisms ⓘ |
| influenced | later developments in categorical factorization theory ⓘ |
| involves | two classes of morphisms ⓘ |
| namedAfter |
Gregory Maxwell Kelly
NERFINISHED
ⓘ
Peter Freyd NERFINISHED ⓘ |
| property | factorization is functorial in many examples ⓘ |
| provides | unifying framework for standard factorization results ⓘ |
| relatedTo |
algebraic weak factorization systems
ⓘ
orthogonality of morphisms ⓘ weak factorization systems ⓘ |
| requiresProperty |
closure of the two classes of morphisms under composition
ⓘ
every morphism factors as a morphism in the first class followed by a morphism in the second class ⓘ lifting properties between the two classes of morphisms ⓘ |
| studiedIn | 2-category theory ⓘ |
| usedFor |
abstracting epi–mono factorizations
ⓘ
abstracting image–coimage factorizations ⓘ organizing factorization theorems in category theory ⓘ |
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: Freyd–Kelly factorization system Description of subject: The Freyd–Kelly factorization system is a concept in category theory that generalizes the idea of factoring morphisms into two classes with specific lifting and composition properties, providing a unifying framework for many standard factorization results.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.