Mixing categories

Oprea, John; Strom, Jeff

doi:10.1090/S0002-9939-2011-10958-4

Mixing categories
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by John Oprea and Jeff Strom PDF

Proc. Amer. Math. Soc. 139 (2011), 3383-3392 Request permission

Abstract:

We show that $\mathrm {cat}(X) \leq \mathrm {cat}_1(X) + \mathrm {cat}^1(X)$, where $\mathrm {cat}_1(X)$ is Fox’s $1$-dimensional category and $\mathrm {cat}^1(X)$ is the $\mathcal {A}$-category of Clapp and Puppe with $\mathcal {A}=\{\mbox {$1$-dimensional spaces}\}$.

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