Vaughan P., vp> ... "never heard of Wikipedia." When five people tell you x is the answer to your question, ... I appreciate your exasperation. Am afraid that almost everyone who replied to my question is severely over-estimating my state of comprehension. My background is primarily in engineering and physics, whereas most of you teach at the honours undergraduate and graduate levels. At present I am trying to understand the concept of map object and the exercises on pp. 314 and 315 of L&S. Long ago, a professional mathematician, as you all are, advised: When stuck, find examples until you come to an understanding. Presently I am looking for examples illustrating Exercises 1-6. Fred's reply is a good start. Longer chains suggested by Matt H. will be interesting, if not necessary. Skipping ahead 34 pages, I see that map objects are an ingredient of a topos. A scan of http://en.wikipedia.org/wiki/Heyting_algebra reports that "map object" is not in the page. Perhaps it should be. Neverthless, working through the book systematically seems more promising than reading about toposes and Heyting algebras before understanding map objects. fwl> ... Heyting's Algebras and one of their possible objective origins. The 2nd edition should correct this omission. I don't want to be presumptuous, but if some of the tiny categories mentioned by Fred and Matt can also fit into the second edition, that would certainly interest me. Without this text, my endeavour to learn category th. would be quite a battle. Thanks! I should have explained at the beginning, the intention in seeking the examples. Sorry for the aggravation. Regards, ... Peter E. http://carnot.yi.org/