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In this talk we will apply the Theorem of Escardó-Flagg [2] characterizing injective objects as algebras for a Kock-Zoberlein monad to the characterization of injective morphisms, making use of a lifting of a Kock-Zoberlein monad to the corresponding slice categories. This result applies in particular in the context of cocomplete (T,V)-categories as studied in [1]. References:
[1] M.M. Clementino, D. Hofmann, Relative injectivity as cocompleteness for a class of distributors, Theory Appl. Categ. 21 (2009), 210-230.
[2] M.H. Escardó, R.C. Flagg, Semantic Domains, injective spaces and monads, Electronic Notes in Theoret. Computer Sci. 20, n. 15 (1999).
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