Whiskering approach to strict 2-categories: literature reference needed I am familiar with the nLab web page that nicely lays out the axioms needed to define strict 2-categories using whiskering as opposed to horizontal composition of 2-cells.  However, I am old fashioned and, when writing an article, would prefer to use a journal reference over a web URL reference.
Does anyone know of a published article that goes over the same material as the following page?
https://ncatlab.org/nlab/show/strict+2-category
Unfortunately that page gives no references.
 A: The formal laws for defining 2-categories along these lines were first spelled out by Godement: 


*

*Roger Godement, Topologie algébrique et theorie des faisceaux, Hermann, Paris, 1958. 


See the "five rules of functorial calculus" given in Appendix 1. Indeed, the horizontal composition of 2-cells is sometimes called the Godement product, and is defined in terms of whiskerings and vertical composites. 
Added: it should be said that Godement was speaking of the functorial calculus specifically of $\text{Cat}$, and did not introduce 2-categories as an abstract notion. My understanding is that it was Ehresmann who introduced 2-categories, as a special case of double categories. 
The notion of sesquicategory formalizes a context in which one has vertical compositions and whiskerings, but one does not have the crucial interchange equation that was singled out by Godement. Thus, a 2-category is a sesquicategory in which the interchange equation is satisfied (giving the horizontal product). Such a development is indicated in 


*

*Ross Street, Categorical Structures, in Handbook of Algebra Vol. 1 (ed. M. Hazewinkel), Elsevier Science, Amsterdam 1996. (pdf)
This would seem to give what you want. 
