Categorists: Here is something which bothers me. It seems to be common for textbook writers to prove that the composite of a pair of monomorphisms is a monomorphism, and it may be taken for granted that everyone knows that every object is a monomorphism. These two facts imply that the monomorphisms in a category form a subcategory of it. A similar remark applies to pullbacks: On page 16 of "Sheaves in Geometry and Logic", Mac Lane and Moerdijk prove among other things that, in the category of commutative squares of a category, the composite of a pair of pullbacks is a pullback, which is a good start toward establishing that the pullbacks form a subcategory of the commutative squares, but Mac Lane and Moerdijk are satisfied with calling the multiplicativity of pullbacks a "pasting lemma" (the quotes are theirs). In proposition 18.16. on page 121 of their 1973 book, "Category Theory", Herrlich and Strecker do this sort of thing wholesale, leaving me to wonder, is there something wrong with the subcategory concept? To be honest, I have noticed that the habit of naming categories after their objects to the extent possible makes it difficult to speak of a subcategory which has the same objects as its parent, but it nevertheless seems strange that, after generalizing the subobject notion, category theory would terminologically orphan its own subobjects. Any clarifications or corrections of these impressions? Pat Donaly