What print color library should I use in illustrator?

Question

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Hello, I am creating illustrations, vector objects in Adobe Illustrator.
I have a question about using color for printing, with digital everything is clear, but in order to create a print for a T-shirt, for example, I think you need to use a specific color library.
Who works in this area, knows the nuances of printing and the requirements of printing houses, enlighten the beginner.
Thank you)

Answer 1

The main thing has already been answered above "CMYK US Web Coated (SWOP) v2" only it is called a color profile, not a color library.
Printer requirements vary greatly. Much also depends on how the printing will be. In general, prepress is a rather time-consuming process and a very extensive topic, which cannot be written in one answer if you do everything the right way.
Well, for example, there is a limitation "the sum of colors in highlights is not lower than 8%, in shadows not higher than 250%" or the total density of colors for coated paper is 300 - this most likely does not tell you anything until you encounter this.
If you print with Pantone, then only them can be used, respectively, etc.
Well, most printing houses accept in pdf format, not ai.

Answer 2

my illustrator teacher said that now the ISO Coated v2
and ISO Coated v2 300% standard
is here
if it doesn’t fit you can use FOGRA39
And each printing house may have its own special requirements, you need to look at their website / call them.
10 commandments when preparing a file for printing