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This is the first part of a series of expository notes on homotopical and categorical algebra. It charts a course from ordinary algebraic structures such as monoids, groups, and rings to their various homotopy-coherent generalizations and equivariant versions. The emphasis is on the ideas that lead to and connect the constructions, as well as where and how they appear in nature.
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Lior Yanovski (2026) studied this question.
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