What are2categories

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=Sni4twL1Bz0

Goal. • Explaining basic concepts of category theory in an intuitive way. • This time. • What are...2-categories? Or: Categories in 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... • 2-categories. • https://en.wikipedia.org/wiki/Strict_... • https://ncatlab.org/nlab/show/2-category • https://arxiv.org/abs/math/0702535 • Bicategories. • https://en.wikipedia.org/wiki/Bicategory • https://ncatlab.org/nlab/show/bicategory • 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. • Picture from https://www.ams.org/journals/tran/194... • Pictures from https://www.dtubbenhauer.com/cat.html • https://en.wikipedia.org/wiki/String_... • https://www.archimedestub.com/tag/eck... • Picture from https://www.dtubbenhauer.com/higherca... • 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

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