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In this work, we provide a model structure on full subcategories of tameobjects in functor categories indexed by continuous realizations of posets ofdimension 1. We also characterize the indecomposable cofibrant objects when thelanding category is the one of bounded non-negative chain complexes. Inaddition, we present a general method to construct indecomposables in a functorcategory by a gluing technique.

Cofibrant indecomposables in chain complex valued tame functors indexed by dimension one posets