On colimits and model structures in various categories of manifolds
David White – GJM, Volume 9, Issue 1 (2024), 1-16.
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- août 24, 2024
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After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then consider various enlargements of our categories of manifolds, culminating in categories of presheaves. We explain how to produce model structures on these enlarged categories, culminating with answering an open problem involving Poincaré spaces.
Milestones:
Received: November 27, 2023
Accepted: April 23, 2024
Revised: May 10, 2024
Authors:
David WhiteDepartment of Mathematics,
Denison University, Granville, Ohio 43023, USA.