OFFSET
0,8
COMMENTS
Specifying a weak factorization system on a poset category is equivalent to specifying a set of morphisms that includes all identity morphisms and is closed under composition and pullback.
LINKS
Hugh Robinson, Table of n, a(n) for n = 0..69
Hugh Robinson, Haskell (ghc 7.4) program to generate the sequence
FORMULA
T(0, n) = T(n, 0) = 1. T(1, n) = T(n, 1) = C(n) the n-th Catalan number (A000108).
EXAMPLE
T(2, 2) = 10: the category has five nonidentity morphisms with relations ca = db = e. a is a pullback of d and of e; b is a pullback of c and of e. So there are ten allowable sets of morphisms: omitting identities for brevity, they are {}, {a}, {b}, {a,b}, {b,c}, {a,d}, {a,b,e}, {a,b,c,e}, {a,b,d,e}, {a,b,c,d,e}.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugh Robinson, Mar 24 2004
EXTENSIONS
More terms from Hugh Robinson, Oct 02 2011
STATUS
approved