Dear categorists, My Ph.D. dissertation, entitled `Dendrotopic Sets for Weak Infinity-Categories', and a preliminary version of my paper `Dendrotopic Sets' can now be downloaded from the web-page www.math.yorku.ca/Who/Grads/palm . The content of the two works is summarized below, where they are referred to as [A] and [B] respectively. Best regards Thorsten Palm ---------------- In his unpublished paper [1], Makkai defined a notion of _weak infinity-category_ (under the name `multitopic omega-category'). The underlying geometric structures, called _multitopic sets_, are described in the three-part paper [2]. Makkai takes a weak infinity-category to be a multitopic set with the mere property that _compositions_ exist, which are defined as equivalences of certain _coslice_ objects. [A] gives a definition of weak infinity-categories equivalent to Makkai's. While this definition falls into the same two stages, it is considerably shorter and more elementary in each of them. The description of the underlying geometric structures, called _dendrotopic sets_ here, is done purely combinatorially (whereas [2] uses the algebraic machinery of multicategories). A coslice object comes in two guises, in both of which it is a dendrotopic set with mild extra structure in the form of a dendrotopic map (whereas in [1] it is a model for a new signature for Makkai's first-order logic with dependent sorts). [A] also presents an alternative method of introducing composition to a dendrotopic set. Here one has to impose the extra structure of a _universality system_: a subset that behaves in such a way that each member can be thought of as a universal arrow. The main theorem of [A] states that a dendrotopic set containing a universality system is a Makkai weak infinity-category. The concept of a dendrotopic set is defined at a more leisurely pace in [B], where the equivalence to the concept of a multitopic set is, indirectly, established. References: [1] M. Makkai: `The multitopic omega-category of all multitopic omega-categories'; mystic.biomed.mcgill.ca/Makkai [2] C. Hermida, M. Makkai, A. J. Power: `On weak higher dimensional categories'; Journal of Pure and Applied Algebra. Part 1: 154 (2000), pp. 221-246; part 2: 157 (2001), pp. 247-277; part 3: 166 (2002), pp. 83-104