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math.AT2018
Euler Characteristics of Finite Homotopy Colimits
John D. Berman
In this short note, we provide a calculation of the Euler characteristic of a finite homotopy colimit of finite cell complexes, which depends only on the Euler characteristics of e…
math.AT2018
Euler characteristic and homotopy cardinality
John D. Berman
Baez asks whether the Euler characteristic (defined for spaces with finite homology) can be reconciled with the homotopy cardinality (defined for spaces with finite homotopy). We c…
math.AG2018
Categorified algebra and equivariant homotopy theory
John D. Berman
This dissertation comprises three collections of results, all united by a common theme. The theme is the study of categories via algebraic techniques, considering categories themse…