Can you "commemorate" something bad?

Commemorate by definition is not "value-neutral".

Commemorate

1. Recall and show respect for (someone or something) in a ceremony.
   "A wreath-laying ceremony to commemorate the war dead."

2. Serve as a memorial to.
   "A stone commemorating a boy who died at sea"

3. Celebrate (an event, a person, or a situation) by doing or building something.

All three definitions are "positive", in that they remember something "good"; i.e. You don't commemorate the Holocaust (unless you think it was a good idea), you commemorate Holocaust victims ("they were 'good' people that died terribly and to make sure something similar doesn't happen again we remember/pay respects to them").

The quality of goodness is very relative. The Nazi's thought the Holocaust was an excellent idea. Obviously everyone else didn't. Had the Nazi's won the Second World War chances are they would commemorate the Holocaust and not the victims, which is opposite to what most countries do today (since the Nazi's lost, their idea of goodness got pretty much wiped off the map). So this can lead to the use of commemorate in situations that may seem backwards to certain people.

Some possible words for the "remembrance of a bad event" could be:

• Dishonor
• Admonish
• Discredit
• Reprimand
• Reproach
• Ridicule
• Mortify
• Disregard

Does an event to be remembered get any worse than this? Go here.

The main commemoration of the 70th anniversary of the liberation of Auschwitz will be held in front of the Death Gate of KL Auschwitz II–Birkenau. On this day – which, for ten years now has been commemorated as International Holocaust Remembrance Day – various anniversary events will be held in many countries: conferences, exhibitions, ceremonies, meetings…

Sure, but offering up a remembrance might be more fitting:

re·mem·brance
rəˈmembrəns
(noun)

    the action of remembering the dead, especially in a ceremony

• https://en.m.wikipedia.org/wiki/Remembrance_Day
• http://www.usatoday.com/story/news/world/2016/05/04/holocaust-remembrance-day-israels-needy-survivors-still-suffer/83913468/

Commemorate is the best available term. Note the prefix Co-, this makes it a group memorial. As in: our group must never forget this extraordinary thing, terrible, or marvelous, as it was.

Group Memory (or commemoration) precedes factions, and factions precede neutrality, (preceding the need for it). Just as a single comma is not a sonnet, nor good or bad.

Commemorate is the best term to use.

Bear in mind you commemorate the past event - not the anniversary.

So you would commemorate the liberation of Auschwitz, which happened 70 years ago.

However, you would not commemorate the 70th anniversary of the liberation of Auschwitz.

I should only say: On this day we remember the Holocaust, never commemorate! English however is not my native language and I may be wrong!