Often, when I won big battles (in Civ4), the one which give strategic advantages, the one I was happy to survive, etc I used to tag one of the tiles where it happened with the name and the date of the battle.

This kind of tag could be interesting for 2 reasons :

1- For the player as it may help to remember these events that build empires, especially when the party lasts hours and hours. 

2- For the game, and the evolution of the culture or the fame... In the reality, it's easy to understand the importance of the battle to build a nation when you see in the capitals, like in Paris or London, how many streets, monuments, places, etc have a name given from a battle... IIn the game, we can imagine that if the winner own the region he could build on this tile a monument to remember this battle, it could give advantages like culture, social cohesion, etc...

The point here is not to tag all the unit killed everywhere, just the real battles between armies of several units and as (if I have well undestood what have been said so far), the battle could last several turn, it could make sense to celebrate the battle with a tag/flag/monument/....?

The tag could be even be enriched with more information via popup after a click on the tag with more details like number of units, number of killed units etc more like EU).

And if ever several battles occured on the same tile (it will surely happen), no problem, we could iterate the battle with number (that's the way it is done in human history). For example, the multiple battle of Isonzo (Italy) in the WWI are named 1st Isonzo to 11th Isonzo battle.

Indeed, This seems like a great Idea, and now that i think about it, seems rather similear to the Total war Series in which the sites of importaint battles are marked by a icon on the map. Perhaps Humankind could also have a similear system with battlefeild sites(that slowly yeild some fame as time goes on) till the discovery of archeology, which then allows for major Resource gains from battle tiles(culture and gold come to mind, due to the cultural significance of some battles and tourism income from sites).

I second the motion.