Nearly every city has a Studio, a building that specializes in monster DNA. They are sometimes called Labs, but because of the bad connotation with that name, it was eventually changed.
The Lab Tech can help you put your monster into cryogenic hibernation (Freezing) or combine its DNA with another monster of your choice (Combining). Sometimes, in-game events occur at the studio. The workers there are often quite knowledgeable about anything involving monster combinations.