Geodesic
$V$-Cat is locally presentable or locally bounded if $V$ is so
Theory and applications of categories, Tome 8 (2001), pp. 555-575

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We show, for a monoidal closed category $V = (V_0,\otimes,I)$, that the category $V$-Cat of small $V$-categories is locally $\lambda$-presentable if $V_0$ is so, and that it is locally $\lambda$-bounded if the closed category $V$ is so, meaning that $V_0$ is locally $\lambda$-bounded and that a side condition involving the monoidal structure is satisfied.

Classification : 18C35, 18D20, 18A32.
Keywords: enriched category, locally presentable category, locally bounded category. 
@article{TAC_2001_8_a22,
     author = {G. M. Kelly and Stephen Lack},
     title = {$V${-Cat} is locally presentable or locally bounded if $V$ is so},
     journal = {Theory and applications of categories},
     pages = {555--575},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a22/}
}
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G. M. Kelly; Stephen Lack. $V$-Cat is locally presentable or locally bounded if $V$ is so. Theory and applications of categories, Tome 8 (2001), pp. 555-575. http://geodesic.mathdoc.fr/item/TAC_2001_8_a22/