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.



Whiskering approach to strict 2-categories: literature reference needed
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)](http://maths.mq.edu.au/~street/45.pdf)


This would seem to give what you want. 


