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Another ketchup improv. 
And shrimp cocktail sauce.

Here you mix a small dollop of orange marmalade, and a small dollop of Patak's Mild Curry paste, into a small amount of tomato paste. Add, in dribs and drabs, some marinara sauce, to thin it somewhat. Then let it sit overnight.
You didn't cook anything, and you made ketchup!
Because of the sugar in marmalade, this may somewhat more closely approximate commercial ketchups with which you are familiar.

For shrimp coctail sauce, you then add a small amount of prepared horseradish, to taste, to either of these recent ketchup recipes.