For　any　triangular　matrix　coalgebra　Γ　=　C　U　0　D,　in　this　paper,　we　first　examine　some　connections　between　coalgebra　properties　of　Γ　and　its　constituent　coalgebras　C,　D,　which　contain　semiperfectness,　computability　and　row/column-finiteness　of　their　left　Cartan　matices.　Then　we　devote　to　considering　the　coresolution　dimensions　of　recollement　of　comodule　categories　by　investigating　covariantly　finite　subcategories.　　©　2023　World　Scientific　Publishing　Company.