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A Course in Homotopical Topology 3.2 - Adjunctions, Co/limits, Monoidal Categories, and Fibrations

In this video, I continue our discussion of category theory by introducing adjunctions, limits and colimits, monoidal categories, and Grothendieck fibrations. This treatment is far from complete, and I may very well end up using more category theory in later videos than I introduced here, so be warned. 00:00:00 - Introduction 00:00:50 - Full, faithful, fully faithful 00:03:42 - Adjunctions 00:13:23 - Examples of adjunctions 00:25:20 - Limits and colimits 00:41:24 - Examples of limits and colimits 00:53:14 - Literally just the definition of left Kan extensions 00:55:34 - Monoidal categories 01:01:23 - Bonus! Grothendieck op/fibrations 01:18:25 - Op/fibrations and pseudofunctors