Derived tensor product

Here is a MWE using semantex. The idea is to use the command key and input the desired command. In this case, you want to over set the L on the symbol. Thus, using command=\overset{L} will suffice.

\documentclass{article}

\usepackage{amsmath,semantex}

\NewSymbolClass\MyBinaryOperator[
    definekeys={
        {Lder}{command=\overset{L}},
        {Rder}{upper=R},
    },
]
\NewObject\MyBinaryOperator\tensor{\otimes}[
    definekeys={
        {der}{Lder},
    },
]
\NewObject\MyBinaryOperator\fibre{\times}[
    % Americans are free to call it \fiber instead
    definekeys={
        {der}{Rder},
    },
]

\begin{document}

\begin{equation}
    A\tensor[R,der] B 
\end{equation}

\end{document}

I don't know how to do it with semantex, but it's not difficult with other tools.

\documentclass{article}
\usepackage{amsmath}
%\usepackage{xparse} % not needed with LaTeX 2020-10-01 or later

\ExplSyntaxOn

\keys_define:nn { cinque/tensor }
 {
  der .tl_set:N = \l__cinque_tensor_upper_tl,
  der .default:n = L,
  unknown .code:n = \tl_set_rescan:Nnx \l__cinque_tensor_subscript_tl { } { \l_keys_key_str },
 }
\tl_new:N \l__cinque_tensor_subscript_tl

\NewDocumentCommand{\tensor}{O{}}
 {
  \group_begin:
  \keys_set:nn { cinque/tensor } { #1 }
  \tl_if_empty:NTF \l__cinque_tensor_upper_tl
   { \otimes }
   { \overset{\l__cinque_tensor_upper_tl}{\otimes} }
  \tl_if_empty:NF \l__cinque_tensor_subscript_tl { \sb{\l__cinque_tensor_subscript_tl} }
  \group_end:
 }

\ExplSyntaxOff

\begin{document}

$A\otimes B$

$A\tensor B$

$A\tensor[R] B$

$A\tensor[der,R] B$

$A\tensor[R,der] B$

$A\tensor[\mathcal{X}] B$

\end{document}

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{xparse}
\usepackage{expl3}
\usepackage{amsmath}

\ExplSyntaxOn
\clist_new:N \l_doc_tmpa_clist
\tl_new:N \l_doc_tmpa_tl
\tl_new:N \l_doc_tmpb_tl

\tl_new:N \g_doc_template_a_tl
\tl_gset:Nn \g_doc_template_a_tl {
  \overset{\tiny L}{*1}
}

\cs_generate_variant:Nn \tl_set_rescan:Nnn {NnV}

\DeclareDocumentCommand{\tensor}{O{}}{
  \clist_set:Nn \l_doc_tmpa_clist {#1}
  \tl_set:Nn \l_doc_tmpa_tl {\otimes}
  
  \clist_map_inline:Nn \l_doc_tmpa_clist {
    \str_case:nn {##1}{
      {der} {
       \tl_set_eq:NN \l_doc_tmpb_tl \g_doc_template_a_tl
       \regex_replace_once:nnN {*1} {\u{\l_doc_tmpa_tl}} \l_doc_tmpb_tl
       \tl_set_eq:NN \l_doc_tmpa_tl \l_doc_tmpb_tl
      }
    }
  }
  
  \clist_map_inline:Nn \l_doc_tmpa_clist {
    \str_case:nn {##1}{
      {R} {
       \tl_set:No \l_doc_tmpa_tl {\l_doc_tmpa_tl \c_math_subscript_token {R}}
      }
    }
  }
  
  \mathbin{\tl_use:N \l_doc_tmpa_tl}
}
\ExplSyntaxOff

\begin{document}

\par $a \tensor[R] b$
\par $a \tensor[R,der] b$
\par $a \tensor[der] b$
\end{document}