function merging / combinator in fsharp

Question

I have a list of functions accepting the same type as an input, different types as output

 [ f_i :  Mytype -> res:Sometype_i ] 

Which operation can merge them into one function of the following type ?

 f : Mytype -> \Product_i Mytype_i

Identically, if I have a list of functions returning the same type

 [ f_i : Mytype_i -> res:Sometype ] 

Which operation can merge them into one function of the following type ?

 f : \Product_i Mytype_i ->  Mytype list

It would be some canonical "preCombinator" or "postCombinator". (I imagine it has a name in FP..)