What are...adjoint functors?
Goal.
Explaining basic concepts of category theory in an intuitive way.
This time.
What are...adjoint functors? Or: Life is not invertible.
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.
Nonsense.
Not sure why I wrote "adjoined" instead of "adjoint" on the title slide. Stupid me, my bad.
Slides.
http://www.dtubbenhauer.com/youtube.html
Website with exercises.
http://www.dtubbenhauer.com/lecture-c...
Adjoint functors.
https://en.wikipedia.org/wiki/Adjoint...
https://ncatlab.org/nlab/show/adjoint...
https://mathworld.wolfram.com/Adjoint...
https://mathoverflow.net/questions/65...
I also used this awesome blog.
https://www.math3ma.com/blog/what-is-...
https://www.math3ma.com/blog/what-is-...
Pictures used.
https://en.wikipedia.org/wiki/Floor_a...
https://en.wikipedia.org/wiki/Floor_a...
https://uploads-ssl.webflow.com/5b1d4...
https://uploads-ssl.webflow.com/5b1d4...
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