This is dual to geometric realization.
But various other operations carry names similar to “totalization”. For instance a total chain complex is related under Dold-Kan correspondence to the diagonal of a bisimplicial set – see Eilenberg-Zilber theorem. As discussed at bisimplicial set, this is weakly homotopy equivalent to the operation that is often called and called the total simplicial set of a bisimplicial set.
To a cosimplicial chain complex we can assign a double complex by taking the alternating sum of the coface maps. Then the totalization of this cosimplicial object and the totalization of the double complex as defined in homological algebra coincide. Moreover, the associated Bousfield-Kan spectral sequence and spectral sequence of a double complex coincide.
Totalization of cosimplicial spaces is discussed in
Review of this includes
Some kind of notes are in