Is there a term, other than “tomato sauce” for a sauce of tomatoes, garlic, onion and perhaps a bit of celery that is simmered for hours on end?
Some would call that a Basic Red Sauce.
Another name is Marinara sauce.
If you include some herbs, like Basil, Thyme, Oregano, that’s pretty much a Napoli sauce (AKA Neapolitan sauce). Celery, and carrot, are pretty common variants.
Carrot? Good Lord!
I learned to add carrot from an Italian woman. I didn’t carrot for it though.
Yep, pretty common in Italian cooking, known as a “battuto” or “soffritto.” I typically see it in meat-based sauces, but you’ll find it in stuff like sugo finto, which is a Tuscan meatless vegetarian tomato sauce, as well.
Don’t knock the carrots, they take some of the excess bite out of tomatoes, making things a tad sweeter. Have had them in meatball calzones, makes a world of difference.
Thanks!
I’m sorry, I wasn’t clear enough–I meant the carrots were chopped up and cooked in the sauce.
Continue cooking!
A New York Italian family I met called their red sauce “gravy.” Long ago an Italian neighbor taught me to make her red sauce, which she called ragu alla bolognese. She used fresh basil, oregano, carrots, celery, onions, garlic, and red wine … and cooked a hambone in it all afternoon. Her daughter would add in a pinch of sugar behind her back, warning me with her eyes to keep quiet. Apparently some think the sugar helps cut the acidity of the tomatoes.
It’s the best I ever tasted … I add sweet Italian sausage and mushrooms to my Okie version …also finely chopped zucchini if my garden runneth over …all the fresh veggies melt down when simmered a long time.
Carrots are an excellent addition to any tomato sauce. They complement the flavor of tomatoes well. Purists can throw in a few big chunks of carrots and remove them later. No one should disregard carrots in tomato sauce until they’ve tried it.
I have seen them, sliced, in Newman’s Own spaghetti sauce.
I feel cheap mentioning that product in such company. 
I thought carrots in a tomato sauce were nasty. I will try mincing them and cooking them away in sauces in the future.
A lot of good cooks keep a jar of store-bought pasta sauce on hand for emergencies, just add your own herbs, sautéed veggies, meat and red wine to make it your own “secret recipe.” A little butter also makes it special.
Fret not, I got that beat: for ages I was using the Walmart (“Great Value”) brand, but lately, it’s really slipped, so I switched to Francesco Rinaldi (meat flavored). Not too bad.
Tomatoes are extremely resilient and versatile.