On the projective model structure on enriched functors for the case of enrichment in the classical model structure on topological spaces:
Robert Piacenza, Homotopy theory of diagrams and CW-complexes over a category, Can. J. Math. Vol 43 (4), 1991 (pdf)
also chapter VI of Peter May et a,, Equivariant homotopy and cohomology theory, 1996 (pdf)
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