B767 Captain reported hydraulic pump failure during departure climb. Flight returned to departure airport and landed safely.

Narrative

After takeoff; when raising the gear; a GEAR DISAGREE and a C HYD DEM PUMP message annunciated on EICAS. From systems knowledge; we expected that the gear would retract but take longer than normal. The FO was PF; and he continued to superbly fly the SID IAW (In Accordance With) our clearance. The gear did retract; and the GEAR DISAGREE message cleared. We retracted the flaps on schedule taking into account an extended retraction time. Once at a safe altitude; we coordinated duties so that we could reference and accomplish the C HYD DEM PUMP checklist. The FO continued PF duties and normal ATC communications; while the Relief Pilot and I did the checklist. Accomplishing the C HYD DEM PUMP checklist confirmed the failure of the center system air demand pump. And there are 4 Notes" associated with that failure. The most critical one to us was the fact that the Hydraulic Motor Generator is not available. Thus; a conference call was made to Dispatch and Maintenance Control to discuss the implications. The HMG (hydraulic Motor Generator) is critically important in the event of a severe electrical failure. All pilots agreed that the safest and wisest course of action was to discontinue our planned ETOPS flight; and land at a suitable airport prior to entering ETOPS airspace. That decision was relayed to Maintenance Control and Dispatch; and Dispatch then conferred with Company Communications System Manager. An air return to ZZZ was recommended and we concurred. We considered the following with respect to our diversion back to ZZZ. We decided that [requesting priority handling] was not warranted. The aircraft was airworthy and not in distress. Fuel Dumping versus Overweight Landing: We decided that an overweight landing would be both safe and doable especially at ZZZ with its long runways; minimal terrain issues landing to the south; and low-density altitude (basically sea-level which helps with landing performance limit weight; ie. go-around capability) at the field. Also; as we worked through all of the above considerations; we kept our Purser and flight attendants aware of the issues we were working. They were doing a drink service which we recommended they complete; but not start the meal service until we had more information and a planned landing airport. Once the decision was made to return to ZZZ; we briefed the Purser directly; gave her time to brief her cabin crew; and then my Relief Pilot made an excellent PA to the customers explaining the decision to return to ZZZ. The FO and I coordinated with ATC for the diversion back to ZZZ. We planned the arrival; approach; and landing with regard to the "Notes" in the C HYD DEM PUMP checklist and decided that I would be the PF for the approach and landing. We accomplished a stable; normal approach and landing at ZZZ. Upon parking at a remote stand; the manager at ZZZ did an absolutely fantastic job with the recovery of our passengers and crew. It was the best handling of an unscheduled arrival and flight cancellation that I have ever experienced. Well done manager All of the above is what happened and how we handled the situation. One major lesson learned in doing the above is that we may have been able to determine if our Air Demand Pump was working on the ground before takeoff. The EICAS message for the C HYD DEM PUMP did annunciate for just a moment as we were doing the After Start flows and checklist (ie. extending the Flaps to 5). The checklist for the C HYD DEM PUMP EICAS message has a "Note" that says "Accomplish this checklist even if the HYD DEM PUMP advisory was displayed only momentarily". I was unaware of that note; and neither of my FO's were either. We discussed the momentary message at the time; but since everything cleared and all appeared to be normal on the overhead panel; we continued normally. But now we know to accomplish this checklist even if the message is displayed only momentarily; and we want ourfellow aviators to know this too."