Difference between revisions of "Monoidal category"
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{{WikiEntry|key=Monoidal category|qCode=1945014}} is a category that admits [[tensor product]]s. [[Bob Coecke]] claims that [[Monoidal Category]] is the [[universal component]] to construct anything, physical or informational<ref>{{:Book/Picturing Quantum Processes}}</ref>. It can be used as the building block for all languages, including natural languages, see [[Quantum Natural Language Processing]]<ref>{{:Video/Bob Coecke, From Quantum Linguistics to Spacetime Linguistics, and Cognition}}</ref>. | {{WikiEntry|key=Monoidal category|qCode=1945014}} is a category that admits [[tensor product]]s. [[Bob Coecke]] claims that [[Monoidal Category]] is the [[universal component]] to construct anything, physical or informational<ref>{{:Book/Picturing Quantum Processes}}</ref>. It can be used as the building block for all languages, including natural languages, see [[Quantum Natural Language Processing]]<ref>{{:Video/Bob Coecke, From Quantum Linguistics to Spacetime Linguistics, and Cognition}}</ref>. | ||
[[Monoidal Category]] is closely related to the concept of [[monad]] | [[Bob Coecke]]'s argument about [[Monoidal Category]] is closely related to the concept of [[monad]] as illustrated in [[Leibniz]]'s [[Monadology]]. It is an important construct that has significant applications in various fields. That means it has direct application to the compilation and interpretation of complex information systems, that covers almost any engineered system of practical interesting. To learn the formal definition of [[Monoidal Category]], [[Richard Borcherds]] has a video on [[Monoidal Category]]<ref>{{:Video/Categories 6 Monoidal categories}}</ref>. | ||
=Monoidal Category as a Two Dimensional Algebra?= | =Monoidal Category as a Two Dimensional Algebra?= | ||
{{:Monoidal Category as a Two Dimensional Algebra}} | {{:Monoidal Category as a Two Dimensional Algebra}} | ||
Revision as of 04:22, 23 March 2022
Monoidal category(Q1945014) is a category that admits tensor products. Bob Coecke claims that Monoidal Category is the universal component to construct anything, physical or informational[1]. It can be used as the building block for all languages, including natural languages, see Quantum Natural Language Processing[2]. Bob Coecke's argument about Monoidal Category is closely related to the concept of monad as illustrated in Leibniz's Monadology. It is an important construct that has significant applications in various fields. That means it has direct application to the compilation and interpretation of complex information systems, that covers almost any engineered system of practical interesting. To learn the formal definition of Monoidal Category, Richard Borcherds has a video on Monoidal Category[3].
Monoidal Category as a Two Dimensional Algebra?
Daniel Tubbenhauer's VisualMath also has a video on What are…monoidal categories?[4]. At the end of the video, he stated that Monoidal Category can be used as a way to model a Two-Dimensional Algebra.
Content related to Monoidal Category:
Monoidal Categories in Visual Representations
Peter Selinger has a paper called: A survey of graphical languages for monoidal categories[5]. There are a few variations of monoidal categories:
Symmetrical Monoidal Category
Braided Monoidal Category
References
- ↑ Coecke, Bob; Kissinger, Aleks (2017). Picturing Quantum Processes. local page: Cambridge University Press. ISBN 978-1316219317.
- ↑ Coecke, Bob (Dec 6, 2021). Bob Coecke, From Quantum Linguistics to Spacetime Linguistics, and Cognition. local page: The Quantum Information Structure of Spacetime.
- ↑ Borcherds, Richard (Oct 10, 2021). Categories 6 Monoidal categories. local page: Richard E. BORCHERDS.
- ↑ Tubbenhauer, Daniel (Feb 27, 2022). What are…monoidal categories?. local page: VisualMath.
- ↑ Selinger, Peter (Aug 23, 2009). A survey of graphical languages for monoidal categories (PDF). local page: arXiv.