This talk is the very first talk for a semester long series on higher algebra. Higher algerbra is the study of algebraic objects in spaces, correcting abnormal behavior of classical homological algebra and encorporating spheres into algebra. In this talk, we will see a concerete example of a higher-algebraic structure on singular cochains, and what structures are needed to formalize such structures with concrete diagrams. We assume familiarity with algebraic topology, category theory and homological algebra (at the first year graduate level).
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