What are...Kan extensions?

Goal. Explaining basics concepts of category theory in an intuitive way. This time. What are...Kan extensions? Or: Recover information; kind of... 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. Warning. There is a typo on the slides. See Spogel's comment below. Slides. http://www.dtubbenhauer.com/youtube.html Kan extensions. https://en.wikipedia.org/wiki/Kan_extension https://ncatlab.org/nlab/show/Kan+extension https://forum.azimuthproject.org/discussion/2267/lecture-50-chapter-3-left-kan-extensions https://bartoszmilewski.com/2017/04/17/kan-extensions/ https://www.euclideanspace.com/maths/discrete/category/principles/universal/kan/index.htm Also Kan extensions, but secretly. Section 3.4 of https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf Pictures used. Picture from https://en.wikipedia.org/wiki/Categories_for_the_Working_Mathematician Some books I am using (I sometimes steal some pictures from there). https://en.wikipedia.org/wiki/Categories_for_the_Working_Mathematician https://www.cambridge.org/core/books/an-introduction-to-category-theory/38C6B02892C2FE7408F52975756AC88D http://www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf https://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf https://math.jhu.edu/~eriehl/context.pdf https://github.com/hmemcpy/milewski-ctfp-pdf Nlab. https://ncatlab.org/nlab/show/HomePage TheCatsters. https://www.youtube.com/channel/UC5Y9H2KDRHZZTWZJtlH4VbA Mathematica. https://wildcatsformma.wordpress.com/ #categorytheory #categoricalalgebra #mathematics