Homotopy Theory with Bornological Coarse Spaces

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Focusing on the foundations of coarse homotopy, this book presents a novel approach to assembly maps through the lens of infinity categories. It introduces bornological coarse spaces and a universal coarse homology theory, employing hybrid structures to bridge large- and small-scale geometry. The text further explores coarse motives of spaces with finite asymptotic dimension and includes examples of coarse homology theories, detailing the coarsification of locally finite homology theories and coarse K-theory, while providing essential background on C*-categories.