05/27/2021, 11:11 PM
John Baez recently gave this short informal talk about monoidal categories.
The video is not long and is intended to be for a general audience (you don't need to be good with algebra or math in general to follow the talk): so don't expect to find formulas, axioms and stuff like that.
Abstract: Scientists and engineers like to describe processes or systems made of smaller pieces using diagrams: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. Many of these diagrams fit into a common framework: the mathematics of symmetric monoidal categories. When we embrace this realization, we start seeing connections between seemingly different subjects. We also get better tools for understanding open systems: systems that interact with their environment. This takes us beyond the old scientific paradigm that emphasizes closed systems.
https://youtu.be/DAGJw7YBy8E
The video is not long and is intended to be for a general audience (you don't need to be good with algebra or math in general to follow the talk): so don't expect to find formulas, axioms and stuff like that.
Abstract: Scientists and engineers like to describe processes or systems made of smaller pieces using diagrams: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. Many of these diagrams fit into a common framework: the mathematics of symmetric monoidal categories. When we embrace this realization, we start seeing connections between seemingly different subjects. We also get better tools for understanding open systems: systems that interact with their environment. This takes us beyond the old scientific paradigm that emphasizes closed systems.
https://youtu.be/DAGJw7YBy8E
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)