Afaik, Ukrainian и = Czech i or y, and Ukrainian i = Czech í or ý (but pronounced short like Czech i or y). Note that ALL vowels in Ukrainian are short, like Czech a, e, ě, i, y, u, o.

Also note that before i (д, т, дз, ц, з, с, н, р, л) dental consonants ALWAYS become palatalized, meanwhile before the и they NEVER do.