Dear People 1. There is now a small web page at URL ftp://triples.math.mcgill.ca/ctrc.html for the Centre de Recherche en Th'eorie des Cat'egories -- Montr'eal. 2. Linked to that web page is my web page and linked to my web page is an expanded and corrected paper on linear time, whose introduction is below. Bon Jour, J. Otto Tensor and Linear Time Introduction Quite simply, serial composition is <--- <--- while parallel composition = tensor is <--- <--- even though we will run both sequentially (section 4.6). Tensor, rather than product, not only provides more models [Huwig 82], but may be necessary at tier 0 in order to avoid the diagonal bug (section 4.6). Roughly, tier 0 is what may go inside loops, while tier 1 is what is defined by loops (section 4.1). By the way, 0-ary serial composition = the identities, while 0-ary parallel composition = the unit. The main text consists of sections 1. Almost Equational Specification, 2. Tensor and System T, 3. Comprehensions and Tiers, 4. Linear Time, and 5. The Linear Time Hierarchy. Section 4 characterizes the linear time functions, using ideas from [Bellantoni-Cook 92, Bloch 92, Leivant-Marion 92], and provides a formal system for them. Section 5 characterizes, improving [Wrathall 78], the linear time hierarchy relations. (These are the Delta_0 relations [H'ajek-Pudl'ak 93, Woods 86].) Section 1, using ideas from [Makkai 94, Ad'amek-Rosick'y 94], explains the almost equational specification which we use throughout. It is based on 2 layers of restricted equational specification: sketches and orthogonality. Section 2 specifies the idealized, but unfeasible, recursion of G"odel's system T, while section 3 provides a means, namely comprehensions and tiers, to attain feasibility. Technical issues have been pushed to the appendices, which are A. Sketches as Presheaves, B. Initial Models, C. Coherence, D. Linear Implication, E. Cotensor, F. Gluing, and G. Turing machines. The main text is hopefully generally readable with perhaps a few glances at say [Barr-Wells 90, 85]. We have used latex2e, xy-pic, and auc-tex.