Closed categories | Monoidal categories
In mathematics, especially in category theory, a closed monoidal category (or a monoidal closed category) is a category that is both a monoidal category and a closed category in such a way that the structures are compatible. A classic example is the category of sets, Set, where the monoidal product of sets and is the usual cartesian product , and the internal Hom is the set of functions from to . A non-cartesian example is the category of vector spaces, K-Vect, over a field . Here the monoidal product is the usual tensor product of vector spaces, and the internal Hom is the vector space of linear maps from one vector space to another. The internal language of closed symmetric monoidal categories is linear logic and the type system is the linear type system. Many examples of closed monoidal categories are symmetric. However, this need not always be the case, as non-symmetric monoidal categories can be encountered in category-theoretic formulations of linguistics; roughly speaking, this is because word-order in natural language matters. (Wikipedia).
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This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
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From playlist Geometry of Frobenioids
Higher Algebra 9: Symmetric monoidal infinity categories
In this video, we introduce the notion of a symmetric monoidal infinity categories and give some examples. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-mu
From playlist Higher Algebra
Category theory for JavaScript programmers #24: monoidal functors
http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
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From playlist Calculus
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From playlist Course 3: Calculus II (Spring 2017)
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
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http://jscategory.wordpress.com/source-code/
From playlist Category theory for JavaScript programmers
On the classification of fusion categories – Sonia Natale – ICM2018
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From playlist Software Development Lectures
Sam Gunningham: Character stacks and (q−)geometric representation theory
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From playlist Topological Cyclic Homology
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From playlist Category Theory