Title: A notion on weak identity arrows in higher categories Abstract: There are a dozen definitions of weak higher categories, all of which loosen the notion of composition of arrows. A new approach is presented here, where instead the notion of identity arrow is weakened --- these are tentatively called fair categories. The approach is simplicial in spirit: while strict higher categories can be described inductively as certain $\Delta\op$-diagrams, the weakening of the identity axiom is obtained by using certain categories of `coloured ordinals' instead of the usual Delta. I'll explain how the definition is almost forced upon us by three standard ideas, and outline some basic properties and guiding conjectures.