This page used to be bigger, but I've chopped it up. This list is an index to the resulting fragments.

- Motivation
- Arrow Lands, HomSets, parallelism and their products.
- Duality
- Arrow Worlds and their simpler properties.
- Transformations, Preconjoinability, full and faithful.
- Composition, factorisation, dual composition, product composition and a
more properties. - Identifiability
- Conjoinability and the resulting Conjoint; Functors.
- Associativity.
- Categories.

Early summer, 1998: I've organised that lot enough that I can state and prove the Yoneda Lemma. This pleases me.

The following stray and garbled section is waiting for me to work out where to put it, which will probably involve a rewrite !.

As an illustration of duality, consider now the definition of a
**Cartesian product**, which I shall not state; instead, I shall
define its dual, the **disjoint union** and leave the reader to
infer the definition of the Cartesian product.

A pair of arrows, (f, h), in a category are said to form a **disjoint
union** precisely if their values under Post are equal and, whenever (d,
j) is a pair of arrows having Post(d) = Post(j) with Prior(d) contained in
Prior(f) and Prior(j) contained in Prior(h) [this will be clearer to readers who
draw the picture], there is a unique arrow d+j in Post(f) with Post(d+j) =
Post(d), which is equal to Post(j), for which (d+j) o f = d and (d+j) o h =
j. In particular, f+h is an identity composable before each of f, h.

When we have such a pair with identities e and c in Prior(f) and Prior(h),
respectively, and a unique identity in Post(f) (which is Post(h)), it is
conventional (by a slight but unambiguous abuse of notation) to call this
identity e+c. Likewise, it is usual to refer to f and h as
**embeddings** f = i_{e} and h = i_{c}. Strictly,
e+c should be denoted i_{e}+i_{c}.

For Cartesian products, the operator + is replaced by × and the pair
of arrows forming the product are known as **projections**
π_{e} and π_{c}, analogously to embeddings; *ie* the
dual of + is × and that of i is π.