Difference between revisions of "Monoidal category"
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{{WikiEntry|key=Monoidal category|qCode=1945014}} is a category that admits [[tensor product]]s. It is an important construct that has significant applications in various fields. In particularly, [[Bob Coecke]]'s work on [[Book/Picturing Quantum Processes|Picturing Quantum Processes]]<ref>{{:Book/Picturing Quantum Processes}}</ref> and [[Quantum Natural Language Processing]]<ref>{{:Video/Bob Coecke, From Quantum Linguistics to Spacetime Linguistics, and Cognition}}</ref> make extensive use of [[Monoidal Category]]. That means it has direct application to compilation and interpretation of complex information systems, that covers almost any engineered system of practical interesting. [[Richard Borcherds]] has a video on [[Monoidal Category]]<ref>{{:Video/Categories 6 Monoidal categories}}</ref>. | {{WikiEntry|key=Monoidal category|qCode=1945014}} is a category that admits [[tensor product]]s. It is closely related to the concept of [[monad]], and some of the philosophical importance can be found in the first few sentences in [[Leibniz]]'s [[Monadology]]. It is an important construct that has significant applications in various fields. In particularly, [[Bob Coecke]]'s work on [[Book/Picturing Quantum Processes|Picturing Quantum Processes]]<ref>{{:Book/Picturing Quantum Processes}}</ref> and [[Quantum Natural Language Processing]]<ref>{{:Video/Bob Coecke, From Quantum Linguistics to Spacetime Linguistics, and Cognition}}</ref> make extensive use of [[Monoidal Category]]. That means it has direct application to compilation and interpretation of complex information systems, that covers almost any engineered system of practical interesting. [[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 11:29, 22 March 2022
Monoidal category(Q1945014) is a category that admits tensor products. It is closely related to the concept of monad, and some of the philosophical importance can be found in the first few sentences in Leibniz's Monadology. It is an important construct that has significant applications in various fields. In particularly, Bob Coecke's work on Picturing Quantum Processes[1] and Quantum Natural Language Processing[2] make extensive use of Monoidal Category. That means it has direct application to compilation and interpretation of complex information systems, that covers almost any engineered system of practical interesting. 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.