What is…duality in categories?

Описание: Goal.
Explaining basic concepts of category theory in an intuitive way.

This time.
What is…duality in categories? Or: Rigid and pivotal categories.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Disclaimer.
The distinction between “large classes” and “small classes (sets)” turns out is crucial for many categorical considerations, but somehow makes the language more cumbersome without too much gain imho. So I will strategically ignore all set-theoretical issues.

Slides.
http://www.dtubbenhauer.com/youtube.html

Website with exercises.
http://www.dtubbenhauer.com/lecture-c...

Rigid and pivotal categories.
https://en.wikipedia.org/wiki/Rigid_c...
https://ncatlab.org/nlab/show/rigid+m...
https://ncatlab.org/nlab/show/pivotal...
https://math.stackexchange.com/questi...

Monoidal categories.
https://en.wikipedia.org/wiki/Monoida...
https://nlab-pages.s3.us-east-2.amazo...
https://ocw.mit.edu/courses/mathemati...
https://www.dtubbenhauer.com/qinvaria...

String diagrams.
https://en.wikipedia.org/wiki/String_...
https://ncatlab.org/nlab/show/string+...
https://core.ac.uk/download/pdf/21747...

Pictures used.
Pictures from From http://www.dtubbenhauer.com/qinvarian...

Some books I am using (I sometimes steal some pictures from there).
https://en.wikipedia.org/wiki/Categor...
https://www.cambridge.org/core/books/...
http://www.tac.mta.ca/tac/reprints/ar...
https://math.mit.edu/~dspivak/teachin...
https://math.jhu.edu/~eriehl/context.pdf
https://github.com/hmemcpy/milewski-c...

Nlab.
https://ncatlab.org/nlab/show/HomePage

TheCatsters.
   / @thecatsters  

Mathematica.
https://wildcatsformma.wordpress.com/

#categorytheory
#categoricalalgebra
#mathematics