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FOUNDATIONS OF THE THEORY OF CATEGORIES
Russian Mathematical Surveys, 1960CONTENTSIntroduction § 1. The definition of a category § 2. Isomorphism. Duality. Functors § 3. Functors of several variables § 4. Subcategories. Concrete categories § 5. Invertible maps. Equivalent objects § 6. Monomorphisms and epimorphisms. Subobjects § 7. Null maps, null objects § 8. Normal monomorphisms and epimorphisms § 9.
Kurosh, A. G. +2 more
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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
Heng Zhao +2 more
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Categorial grammar and type theory
Journal of Philosophical Logic, 1990La grammaire categorielle est revelatrice d'un large ensemble de relations entre la logique mathematique et la linguistique. L'A. insiste sur le fait que les travaux de nature descriptive aussi bien que les travaux de nature computationnelle ont contribue a etablir ces ...
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2005
This paper describes some experiments in using algebraic and categorical ideas to write programs. In particular a program to compute colimits in a category given coproducts and coequalisers has been written, also one to ‘lift’ such colimits to comma categories.
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This paper describes some experiments in using algebraic and categorical ideas to write programs. In particular a program to compute colimits in a category given coproducts and coequalisers has been written, also one to ‘lift’ such colimits to comma categories.
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2020
This chapter aims to introduce sufficient category theory to enable a formal understanding of the rest of the book. It first introduces the fundamental notion of a category. It then introduces functors, which are maps between categories. Next it introduces natural transformations, which are natural ways of mapping between functors.
Ash Asudeh, Gianluca Giorgolo
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This chapter aims to introduce sufficient category theory to enable a formal understanding of the rest of the book. It first introduces the fundamental notion of a category. It then introduces functors, which are maps between categories. Next it introduces natural transformations, which are natural ways of mapping between functors.
Ash Asudeh, Gianluca Giorgolo
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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.
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Application of category theory
Ingénierie des systèmes d'information, 2018Maribel Mendonça +2 more
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Groupoids and skeletal categories form a pretorsion theory in
Advances in Mathematics, 2023Marino Gran +2 more
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The Representation Theory of Brauer Categories I: Triangular Categories
Applied Categorical Structures, 2022Steven V Sam, Andrew W. Snowden
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