What do (lambda) function closures capture?

you may force the capture of a variable using an argument with a default value:

>>> for i in [0,1,2,3]:
...    adders[i]=lambda a,i=i: i+a  # note the dummy parameter with a default value
...
>>> print( adders[1](3) )
4

the idea is to declare a parameter (cleverly named i) and give it a default value of the variable you want to capture (the value of i)

What do the closures capture exactly?

Closures in Python use lexical scoping: they remember the name and scope of the closed-over variable where it is created. However, they are still late binding: the name is looked up when the code in the closure is used, not when the closure is created. Since all the functions in your example are created in the same scope and use the same variable name, they always refer to the same variable.

There are at least two ways to get early binding instead:

1. The most concise, but not strictly equivalent way is the one recommended by Adrien Plisson. Create a lambda with an extra argument, and set the extra argument's default value to the object you want preserved.

2. More verbosely but also more robustly, we can create a new scope for each created lambda:

   >>> adders = [0,1,2,3]
   >>> for i in [0,1,2,3]:
   ...     adders[i] = (lambda b: lambda a: b + a)(i)
   ...     
   >>> adders[1](3)
   4
   >>> adders[2](3)
   5
   

   The scope here is created using a new function (another lambda, for brevity), which binds its argument, and passing the value you want to bind as the argument. In real code, though, you most likely will have an ordinary function instead of the lambda to create the new scope:

   def createAdder(x):
       return lambda y: y + x
   adders = [createAdder(i) for i in range(4)]
   

For completeness another answer to your second question: You could use partial in the functools module.

With importing add from operator as Chris Lutz proposed the example becomes:

from functools import partial
from operator import add   # add(a, b) -- Same as a + b.

adders = [0,1,2,3]
for i in [0,1,2,3]:
    # store callable object with first argument given as (current) i
    adders[i] = partial(add, i) 

print adders[1](3)