In this talk we investigate the notion of normed category: a category  where each hom-set \( X(A,B) \) comes equipped with a norm \( X(A,B)\to [0, \infty] \), subject to suitable axioms. As suggested by Lawvere (1973), we treat normed categories consequentially as categories enriched in...

In broad terms, the main goal of homotopy theory is to study the objects of a category up to a "weak equivalence". These weak equivalences satisfy certain properties, that are also satisfied by isomorphisms, but with the downside that they are not always invertible. Thus, over the years,...

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