Results 321 to 330 of about 8,103,242 (367)
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, 2022
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated.
E. Riehl, Dominic R. Verity
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The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated.
E. Riehl, Dominic R. Verity
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Category Theory for Optimization
2018 IEEE 12th International Conference on Semantic Computing (ICSC), 2018This paper shows how concepts coming from category theory can help to improve the algorithms dealing with large set of data. Data structures can be modeled by functors that are related by natural transformations usable both to reduce data size or to shift an algorithm applicable to a particular data structure to an equivalent algorithm for another data
Michel Hassenforder +2 more
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Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering
, 2017: In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category.
M. A. Mabrok, M. Ryan
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Experience Implementing a Performant Category-Theory Library in Coq
International Conference on Interactive Theorem Proving, 2014We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large ...
Jason Gross +2 more
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2021
[en] The main goal of this project is the investigation of the mathematical structures called categories, looking at their most important features and applications. It will also be see the concept of functors, how they make sense when working with categories and two of the most relevant type of functors, representable and adjoint functors.
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[en] The main goal of this project is the investigation of the mathematical structures called categories, looking at their most important features and applications. It will also be see the concept of functors, how they make sense when working with categories and two of the most relevant type of functors, representable and adjoint functors.
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Category Theory for the Sciences
, 2014Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics.
David I. Spivak
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, 2014
Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
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Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
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Lawvere's basic theory of the category of categories
Journal of Symbolic Logic, 1975It is long known that Lawvere's theory in The category of categories as foundations of mathematics A[1] does not work, as indicated in Ishell's review [0]. Isbell there gives a counterexample that CDT—Category Description Theorem—[1, p. 15] is in fact not a theorem of BT (the Basic Theory of [1]) and suggests adding CDT to the axioms.Our starting point
Anne Preller, Georges Blanc
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Coherence in Three-Dimensional Category Theory
, 2013Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape.
N. Gurski
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2011
Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning.
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Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning.
openaire +2 more sources