Axiomatic shape theory

Bacon, Philip

doi:10.1090/S0002-9939-1975-0420611-2

Axiomatic shape theory
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Proc. Amer. Math. Soc. 53 (1975), 489-496 Request permission

Abstract:

The notion of shape theory is so defined that, if ${\text {H}}$ is a category and ${\text {W}}$ is a subcategory of ${\text {H}}$, all shape theories on $({\text {H,}}\;{\text {W}})$ are isomorphic and, under a mild condition, a shape theory on $({\text {H,}}\;{\text {W}})$ always exists. Additional theorems facilitate the comparison of shape theories constructed by various means.

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