Sheaves in Geometry and Logic
E157405
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Sheaves in Geometry and Logic canonical | 4 |
| A First Introduction to Topos Theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382994 — 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: Sheaves in Geometry and Logic Context triple: [Saunders Mac Lane, notableWork, Sheaves in Geometry and Logic]
-
A.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
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.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
-
D.
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.
-
E.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
- 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: Sheaves in Geometry and Logic Target entity description: 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.
-
A.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
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.
Kronecker’s finitism
Kronecker’s finitism is a philosophical and mathematical stance asserting that only finite, constructible mathematical objects and proofs are legitimate, rejecting the existence of actual infinities.
-
D.
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.
-
E.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| aim |
to provide a first introduction to topos theory
ⓘ
to relate geometry and logic via sheaf and topos theory ⓘ |
| author |
Ieke Moerdijk
ⓘ
Saunders Mac Lane ⓘ |
| countryOfPublication | Germany ⓘ |
| field |
algebraic geometry
ⓘ
category theory ⓘ foundations of mathematics ⓘ mathematical logic ⓘ sheaf theory ⓘ topos theory ⓘ |
| firstPublicationYear | 1992 ⓘ |
| hasISBN |
0-387-97710-4
ⓘ
978-0-387-97710-2 ⓘ |
| hasPart |
applications to geometry
ⓘ
applications to logic and model theory ⓘ construction of Grothendieck toposes ⓘ development of sheaf theory ⓘ discussion of internal language and logic ⓘ introduction to category theory ⓘ treatment of elementary toposes ⓘ |
| hasSubtitle |
A First Introduction to Topos Theory
ⓘ
linked to:
Sheaves in Geometry and Logic
|
| hasTitle | Sheaves in Geometry and Logic ⓘ |
| influenced |
foundational studies in mathematics
ⓘ
research in categorical logic ⓘ research in topos theory ⓘ |
| language | English ⓘ |
| publisher |
Springer-Verlag
ⓘ
linked to:
Springer
|
| relatedTo |
Categories for the Working Mathematician
ⓘ
Topos Theory ⓘ
linked to:
Grothendieck toposes
|
| series |
Universitext
ⓘ
linked to:
Springer
|
| subject |
Grothendieck toposes
ⓘ
categorical foundations ⓘ cohomology via sheaves ⓘ elementary toposes ⓘ geometric morphisms ⓘ internal logic of a topos ⓘ intuitionistic logic ⓘ logical completeness theorems in toposes ⓘ model theory in toposes ⓘ sheaves ⓘ sites and Grothendieck topologies ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
researchers in category theory and logic ⓘ |
| usedAs |
graduate textbook
ⓘ
reference work in topos 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: Sheaves in Geometry and Logic Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Sheaves in Geometry and Logic