On functors which are lax epimorphisms (Q2755055)

Laxly epimorphic functors are the representably fully faithful morphisms in the opposite of the 2-category of categories. In Example 4.5 on page 439 of \textit{B. J. Day}'s paper [Bull. Aust. Math. Soc. 16, 427-448 (1977; Zbl 0359.18009)] these functors were called Cauchy dense. The present paper defines lax epimorphic functors, gives three equivalent characterizations, compares them with pseudoepimorphisms, examines what happens when the categories are ordered sets, provides some technical examples, and, gives three equivalent characterizations of a larger class of functors.