The Commissioner gives approval to an insurer to do business in Colorado in a certificate of:

The correct choice is authority, as a certificate of authority is a formal document issued by a state's insurance commissioner that grants an insurance company the right to operate and transact insurance business within that state. This certificate ensures that the insurer has met all necessary regulations, licensing requirements, and financial standards set forth by the state, thereby protecting policyholders and maintaining the integrity of the insurance market.

The other options do not align with the definition and function of the certificate in question. A certificate of convenience often relates to approval for operating a service or business entity in a more general sense, whereas a certificate of admittance is not a recognized term in the context of insurance licensing and does not specifically refer to insurers. A certificate of agency typically refers to permissions given to agents or representatives to act on behalf of another party, not to insurers themselves. Thus, the distinction is important, as it clarifies that the power to conduct insurance activities in the state originates from the certificate of authority issued by the Commissioner.