I am trying to wrap my mind around Tannaka-Krein duality and it seems quite mysterious for me, as well, as its history. So let me ask:

**Question:** What was the motivation and historical context for works of major contributors to the "Tannaka-Krein theory" (in a broad sense) ? 
Just to name a few names: Tannaka, Krein, Saavedra, Deligne, Milne, Lurie, (it seems Grothendieck should also be in this list (?) ).

Let me explain some points in the history which seems to me puzzling:

 
**1)** [Mark Krein][1] was a famous Soviet mathematician, but he was an expert in analysis, it seems it is the only paper by him devoted to algebra. How did he come to it ? Why did not continue ? 

**2)** Similar question about  
Tadao Tannaka. ["His interest in mathematics lied mainly in algebraic number theory" ][2], 
And it seems similar to Krein, it is the only work by devoted to group theory. (See his [publication list][3]). 

**3)** P. Deligne seems devoted quite much efforts on "Tannakian formalism"  and more generally on tensor categories. What was his motivation ? He is leading algebraic geometer. 
So probably the subj. should be quite important in algebraic geometry ? What is its importance ? 

**4)** [Wikipedia article][4] starts with a sentence: "... natural extension to the non-Abelian case is the Grothendieck duality theory." What is the role of Grothendieck in this history ? And what is "Grothendieck duality theory" - wikipedia links to something not related. 
 
**5)** Important work was done by [Saavedra][5]. Seems not so much is known about him,
his motivation, his other works.

**6)** J. Lurie seems to develop the theory further (see e.g. [MO question Tannakian formalism][6]). What is motivation ? 


  [1]: http://en.wikipedia.org/wiki/Mark_Krein
  [2]: http://projecteuclid.org/download/pdf_1/euclid.tmj/1178228363
  [3]: http://projecteuclid.org/download/pdf_1/euclid.tmj/1178228363
  [4]: http://en.wikipedia.org/wiki/Tannaka%E2%80%93Krein_duality
  [5]: http://mathoverflow.net/questions/107095/saavedras-definition-of-tannakian-category
  [6]: http://mathoverflow.net/questions/3446/tannakian-formalism