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Approximate categorical structures

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Abdelkrim Aliouche and Carlos Simpson

We consider notions of metrized categories, and then approximate
categorical structures defined by a function of three variables
generalizing the notion of 2-metric space. We prove an embedding theorem
giving sufficient conditions for an approximate categorical structure to
come from an inclusion into a metrized category.

Keywords:
metric, $2$-metric space, category, functor, Yoneda embedding, bimodule,
path, triangle

2010 MSC:
Primary 18A05; Secondary 54E35, 08A72

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 44, pp 1522-1562.

Published 2017-12-18.

http://www.tac.mta.ca/tac/volumes/32/44/32-44.pdf

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