Abstract
Weak equivalence is defined as equivalence in the bicategory of modules between internal categories. It is known that two categories are weakly equivalent if and only if their Cauchy completions are equivalent. We prove that this condition can be generalized to a suitable notion of intermediate category, stable under composition with weak equivalences. Applications to categorical Morita theory are given.
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Betti, R. Weak Equivalence of Internal Categories. Applied Categorical Structures 8, 307–316 (2000). https://doi.org/10.1023/A:1008732224512
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DOI: https://doi.org/10.1023/A:1008732224512