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Categories applied to passive electrical circuits analysis - A Study/Discussion Group

edited May 2018

Considering an implicit reduction of abstraction by it´s mechanical analogs , for me , to study categories on the frame of simple RLC circuits is also an auxiliary interesting way to step in to applied category theory . I´ve been reading:

https://johncarlosbaez.wordpress.com/2014/10/03/network-theory-part-30/

https://arxiv.org/abs/1504.05625

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1.
edited May 2018
Comment Source:http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf https://johncarlosbaez.wordpress.com/2018/05/19/circuits-bond-graphs-and-signal-flow-diagrams/
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2.
edited May 2018

reproducing some Prof Baez tips:

"Any introduction to category theory contains these insights; two of my favorites are these free ones:

Tom Leinster, Basic Category Theory, Cambridge Studies in Advanced Mathematics, Vol. 143, Cambridge University Press, 2014. (An introduction.)

Emily Riehl, Category Theory in Context, Dover, New York, 2016. (More advanced.)

However, it's hard to get these insights without carefully studying several of these books and also talking to an expert several times a week for a long time. That's why I'm teaching this 6-month-long course!" https://forum.azimuthproject.org/discussion/comment/18302/#Comment_18302

"One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps between gadgets of this kind. For example, when you think about sets you should also think about functions. When you think about vector spaces you should also think about linear maps. And so on." https://forum.azimuthproject.org/discussion/2095/lecture-26-chapter-2-monoidal-monotones/p1

https://forum.azimuthproject.org/discussion/comment/18440/#Comment_18440

Comment Source:reproducing some Prof Baez tips: "Any introduction to category theory contains these insights; two of my favorites are these free ones: Tom Leinster, Basic Category Theory, Cambridge Studies in Advanced Mathematics, Vol. 143, Cambridge University Press, 2014. (An introduction.) Emily Riehl, Category Theory in Context, Dover, New York, 2016. (More advanced.) However, it's hard to get these insights without carefully studying several of these books and also talking to an expert several times a week for a long time. That's why I'm teaching this 6-month-long course!" https://forum.azimuthproject.org/discussion/comment/18302/#Comment_18302 "One of the main lessons of category theory is that whenever you think about some kind of mathematical gadget, you should also think about maps between gadgets of this kind. For example, when you think about sets you should also think about functions. When you think about vector spaces you should also think about linear maps. And so on." https://forum.azimuthproject.org/discussion/2095/lecture-26-chapter-2-monoidal-monotones/p1 https://forum.azimuthproject.org/discussion/comment/18440/#Comment_18440
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edited May 2018
Comment Source:Another interesting text by Prof Baez http://math.ucr.edu/home/baez/categories.html http://math.ucr.edu/home/baez/topos.html
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4.

Hey thanks a ton, https://arxiv.org/abs/1504.05625 was exactly what i was looking for.

Comment Source: Hey thanks a ton, https://arxiv.org/abs/1504.05625 was exactly what i was looking for.
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5.

You are welcome

Comment Source:You are welcome
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6.
edited May 2018
Comment Source:https://forum.azimuthproject.org/discussion/comment/18779/#Comment_18779 Slides Coya thesis' defense Thesis- http://math.ucr.edu/home/baez/thesis_coya.pdf
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7.
edited July 2018

John´s tips:

"Here are two important principles of category theory:

Every collection of things is eager to become the objects of a category.

and

Every map sending things of one kind to things of another kind is eager to become a functor."

Comment Source:https://forum.azimuthproject.org/discussion/comment/18673/#Comment_18673 https://forum.azimuthproject.org/discussion/comment/18947/#Comment_18947 John´s tips: "Here are two important principles of category theory: Every collection of things is eager to become the objects of a category. and Every map sending things of one kind to things of another kind is eager to become a functor." 
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8.
edited July 2018

forum.azimuthproject.org/discussion/2294/sorry-no-lecture-on-wednesday#latest

Paper - eletric circuits

Comment Source:forum.azimuthproject.org/discussion/2294/sorry-no-lecture-on-wednesday#latest Paper - eletric circuits
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9.
edited August 2018
Comment Source:https://forum.azimuthproject.org/discussion/comment/20620/#Comment_20620 http://math.ucr.edu/home/baez/qg-winter2001/definitions.pdf http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005683 https://www.diva-portal.org/smash/get/diva2:1206380/FULLTEXT01.pdf