I'm searching the wheres and whys about the integral notation for co/[ends](http://ncatlab.org/nlab/show/end). Who was the first to adopt it? Can you give me a precise pointer or tell me the whole story about it? Was s/he motivated by the Fubini rule only, or there is another additional reason?


Thanks a lot!



History of integral notation for coends
From Ross Street's *An Australian conspectus of higher categories*:



> 
> Kelly developed the theory of enriched categories describing enriched adjunction and introducing the variety of limit he called *end*. I later pointed out that Yoneda had used this concept in the special case of additive categories using an *integral notation* which Brian Day and Max Kelly adopted. Following this, Mac Lane discussed ends for ordinary categories.
> 
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The Day-Kelly paper referred to is 


B. Day and G.M. Kelly, Enriched functor categories, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 178–191. 


whose introduction states



> 
> What we call ends and coends were introduced in the case $V = \text{Ab}$ by Yoneda; we borrow from him the "integral notation". 
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> 
> 


The Yoneda paper referred to is 


Yoneda, N., On Ext and exact sequences. Jour. Fac. Sci. Univ. Tokyo 8 (1960), 507 - 576.


where we find written on page 546 (thanks to Francesco for the page reference)



> 
> We shall write $\int\_C H$ for the integration $I$ of $H$, and $\int\_C^\ast H$ for the cointegration $J$ of $H$.
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> 
> 


where his "integration" is our "coend", and dually.


