Statements (137)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematician
|
| gptkbp:bfsLayer |
4
|
| gptkbp:bfsParent |
gptkb:Natalia_Voevodsky
|
| gptkbp:applies_to |
gptkb:philosopher
gptkb:physicist gptkb:product gptkb:collection Algebra |
| gptkbp:developed_by |
gptkb:William_Lawvere
gptkb:F._William_Lawvere 1960s |
| gptkbp:enables |
Interpretation of Logic
Interpretation of Set Theory Interpretation of Topology |
| gptkbp:field_of_study |
gptkb:product
|
| gptkbp:has_feature |
Objects
Morphisms Functors |
| gptkbp:has_influence_on |
gptkb:Mathematician
Metamathematics |
| gptkbp:has_programs |
gptkb:philosopher
gptkb:physicist gptkb:Artificial_Intelligence gptkb:Mathematician gptkb:currency Computer Science Information Theory |
| gptkbp:has_role |
gptkb:Constructive_Mathematics
Higher Category Theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Topos Theory
|
| gptkbp:is_a_framework_for |
gptkb:musician
gptkb:military_officer gptkb:political_movement |
| gptkbp:is_associated_with |
gptkb:Grothendieck
gptkb:Lawvere gptkb:operating_system Sheaves Topos Theory in Algebra Topos Theory in Computer Science Topos Theory in Logic Topos Theory in Philosophy Topos Theory in Physics |
| gptkbp:is_characterized_by |
gptkb:Higher_Dimensional_Categories
gptkb:Topoi gptkb:Grothendieck_Toposes Logical Frameworks Functors Natural Transformations Categorical Logic Adjunctions Internal Logic Elementary Toposes Exponentials Limits and Colimits Monoids in Toposes Subobject Classifier Topos Morphisms Topos Theory and Set Theory |
| gptkbp:is_connected_to |
gptkb:plant
gptkb:Higher_Dimensional_Categories Model Theory Structuralism Type Theory Constructivism Topological Spaces Intuitionism Sheaf Theory Formalism Homotopy Theory Categorical Logic Quantum Logic Categorical Topology Functorial Semantics Functoriality in Mathematics |
| gptkbp:is_considered |
Philosophical Discussions
Mathematical Discussions |
| gptkbp:is_considered_as |
A basis for modern mathematics
A bridge between mathematics and philosophy A foundation for categorical logic A foundation for mathematics A tool for abstraction A unifying framework |
| gptkbp:is_explored_in |
Philosophical Inquiry
Philosophical Literature Mathematical Literature Mathematical Inquiry |
| gptkbp:is_influenced_by |
gptkb:plant
gptkb:collection Model Theory Type Theory Algebraic Topology Sheaf Theory Homotopy Theory Category Theory Foundations Grothendieck's Work |
| gptkbp:is_part_of |
Mathematical Logic
Abstract Algebra Mathematical Analysis Mathematical Structures Foundations of Mathematics |
| gptkbp:is_related_to |
gptkb:Homotopy_Type_Theory
Functoriality Sheaf Theory Homotopy Theory Higher Category Theory |
| gptkbp:is_studied_in |
gptkb:product
Mathematical Logic Mathematicians Physicists Computer Scientists Algebraic Topology Philosophy Departments Logicians Mathematics Departments |
| gptkbp:is_used_in |
gptkb:plant
gptkb:Mathematician gptkb:Homotopy_Type_Theory Theoretical Computer Science Mathematical Physics Type Theory Homotopy Theory |
| gptkbp:is_used_to |
Explore Mathematical Structures
Model Set Theory Model Type Theory Study Logical Foundations |
| gptkbp:provides |
A framework for interpreting logical theories
A generalization of set theory A framework for interpreting logical systems |
| gptkbp:related_concept |
Limits
Functoriality Colimits Sheaves Presheaves |
| gptkbp:related_to |
gptkb:plant
gptkb:product gptkb:collection Homotopy Theory |