doesnt the 0-dim vector space carry the final (terminal) coalgebra? (it has just one vector, so there is not much choice for v_0 and v_1.) -- dusko Tom Leinster wrote:
Here's a question belonging to (10), to which I don't know the answer. Let C be the category whose objects are triples (V, v_0, v_1) where V is a vector space and v_0 and v_1 are linearly independent vectors in V, and whose maps preserve linear structure and the `basepoints'. There's a `wedge' functor C x C --> C defined by
(V, v_0, v_1) wedge (W, w_0, w_1) = ( (V + W)/~, v_0, w_1)
where (V + W)/~ is the direct sum with v_1 identified with w_0. (So dim(V wedge W) = dim V + dim W - 1.) There's then an endofunctor G of C given by self-wedging. Question: what, if any, is the terminal G-coalgebra?
(I suspect the answer is something to do with measure/integration - again see Peter's previous postings - but really have no idea.)
Finally, re citations: I'll stick in a Pavlovic-Pratt reference, as suggested.
All the best, Tom
30-Nov-2004 08:04:37 -0400,3767;000000000000-00000000