Abstract
The paper introduces some mild requirements under which a Kan extension is a full embedding that preserves factorization systems and colimits of α-directed diagrams. The existence of such Kan extensions is then used to establish conditions equivalent to algebraic universality of concrete categories such as varieties of algebras of any given similarity type.
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Koubek, V., Sichler, J. On Full and Faithful Kan Extensions. Applied Categorical Structures 6, 291–332 (1998). https://doi.org/10.1023/A:1008681922458
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DOI: https://doi.org/10.1023/A:1008681922458