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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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Category Theory and Theory of Evolution
Lobachevskii Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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A n theory, L.S. category, and strong category
Mathematische Zeitschrift, 2007For every space \(X\) there is a Ganea-Svarz fibration \((\Omega X)^{*(n+1)}\to B_n\Omega X \to X\), and it is clear that the functor \(B_n\Omega\) is a comonad. The author introduces the notion of a weak homotopy space over \(B_n\Omega\) and proves that if \(X\) admits such a structure, then cat(\(X\))=Cat(\(X\)) under some dimensional and ...
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2020
In this chapter, we define and then study in detail Tamarkin categories. A Tamarkin category is defined as a categorical orthogonal complement, and the elements in a Tamarkin category can be completely characterized by a sheaf operator - sheaf convolution.
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In this chapter, we define and then study in detail Tamarkin categories. A Tamarkin category is defined as a categorical orthogonal complement, and the elements in a Tamarkin category can be completely characterized by a sheaf operator - sheaf convolution.
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