[
left{ begin{gathered}text{text 1}\
text{text 2}\
A=B
end{gathered}
right} rightleftarrowsleft{ begin{gathered}text{some text here}\
text{and here}
end{gathered}
right} ,
]

[
xymatrix{left{ text{text}right} ar@/^{1pc}/[r] & ar@/^{1pc}/[l]left{ text{more text}right} }
]

documentclass{article}
usepackage{amsmath}
usepackage[all,cmtip]{xy}

begin{document}

[
xymatrix{
  {begin{Bmatrix}text{text a}\text{text b}end{Bmatrix}}
  ar@/^{1pc}/[r] &
  {begin{Bmatrix}text{text a}\text{text b}\text{text c}end{Bmatrix}}
  ar@/^{1pc}/[l]
}
]

end{document}

documentclass[a4paper,12pt]{article}
usepackage{mathtools}
usepackage[all]{xy}
begin{document}

xymatrix@C=3pc{{left{begin{aligned}
text{text a}\
text{text b}
end{aligned}right}
} ar@/^{1.5pc}/[r] & ar@/^{1.5pc}/[l]{left{begin{aligned}
text{text a}\
text{text b}\
text{text c}\
end{aligned}right}
}}
end{document}

documentclass[a4paper,12pt]{article}
usepackage{tikz-cd}
usepackage{amsmath}
begin{document}
begin{tikzcd}
left{begin{array}{lr} text{text a} \    text{text b} \     end{array}right}   arrow[r, bend left=15] & left{begin{array}{lr} text{text a} \    text{text b} \    text{text c} \ end{array}right} arrow[l, bend left=15]
end{tikzcd}
end{document}