Cfrgtkky

I am trying to figure out how to draw composition in a multicategory using same depiction used in Leinster's book "Higher Operads, Higher Categories". Here is what I am trying to draw:

I did something similar, but I could not do it completely. Here is what I got

documentclass{article}

usepackage[all]{xy}

begin{document}

    xymatrix{

      a1 ar@{-}[r] & ar@{-}[dd] ar@{-}[dr]  &            & \

      a2 ar@{-}[r] &                          & ar@{-}[r] & a \

      a3 ar@{-}[r] & ar@{-}[ur]              &            & 

    }

end{document}

Any help would be greatly appreciated.

Here is a very similar picture that can be tweaked accordingly. In my document, all lines are adjacent to the triangles but I didn't want to include all my preamble; the positions of wires are inserted `manually' so they can easily change.

documentclass[11pt]{amsart}



usepackage[a4paper,top=3cm,bottom=3cm,inner=3cm,outer=3cm]{geometry}

usepackage{tikz}

usetikzlibrary{positioning,decorations.markings,arrows.meta,calc,fit,quotes,cd,math,arrows,backgrounds,shapes.geometric}



begin{document}





begin{displaymath}

begin{tikzpicture}[triangle/.style = {fill=gray!20, regular polygon, regular polygon sides=3}]

path (0,0) node [triangle,draw,shape border rotate=-90,inner sep=0pt,label=178:$vdots$] (a) {$theta_n$} (0,4) node [triangle,draw,shape border rotate=-90,inner sep=0pt,label=178:$vdots$] (b) {$theta_1$} (3,2) node [triangle,draw,shape border rotate=-90,label=135:$a_1$,label=230:$a_n$,label=178:$vdots$] (c) {$theta$} (9,2) node [triangle,draw,shape border rotate=-90,inner sep=-25pt,label=178:$vdots$] (d) {$qquadthetacirc(theta_1,ldots,theta_n)$};

draw [-] (a) .. controls +(right:2cm) and +(left:1cm).. (c.220);

draw [-] (b) .. controls +(right:2cm) and +(left:1cm).. (c.140);

draw [-] (d) to node [above] {$a$} (11.7,2);

draw [-] (c) to node [above] {$a$} (4,2);

draw [-] (7.2,3.5) to node [above] {$a_{11}$} (7.85,3.5);

draw [-] (7.2,.5) to node [below] {$a_{nk_n}$} (7.85,.5);

draw [-] (-.85,4.3) to node [above] {$a_{11}$} (-.3,4.3);

draw [-] (-.85,3.6) to node [below] {$a_{1k_1}$} (-.3,3.6);

draw [-] (-.85,0.3) to node [above] {$a_{n1}$} (-.3,0.3);

draw [-] (-.85,-0.4) to node [below] {$a_{nk_n}$} (-.3,-0.4);

node () at (5.5,2) {$mapsto$};

end{tikzpicture}

end{displaymath}

end{document}