P.20 of Prof. Taylor's book briefly recounts the history of "function" as a (rigorously formulated) expression for numerical calculation using arithmetic and transcendental operations. More generally, Cox et al in "Ideals, Varieties, and Algorithms" define "algorithm" as a (rigorously formulated) set of instructions for manipulating input expressions resulting in output expressions. Algorithms may be presented in "pseudocode" as a prelude to implementation in a particular computer programming language such as Maple, or Haskell. Mac Lane-Moerdijk define an elementary (Lawvere-Tierney) topos to be a category with finite limits, finite colimits, exponentials, and a subobject classifier. So to prove a category is a topos it is necessary to prove that it has a subobject classifier. My query was stimulated by Lawvere-Schanuel in "Conceptual Mathematics" pp.340-341 proof that the category of directed graphs has a subobject classifier. They give a finite list of the possibilities for an element of a graph (dot or arrow) to belong to a subgraph. It seems to me such a list could be generated by an algorithm. Then there is a step explained by pictures leading to Omega(DirectedGraph). To me this hints at an algorithm too. Ellis D. Cooper [For admin and other information see: http://www.mta.ca/~cat-dist/ ]