7 Mar
2009
7 Mar
'09
6:15 a.m.
Given a category A, the Isbell envelope E(A) is the category whose objects are triplets (F_*, F^*, t) where F_* : A --> Set and F^* : A^{op} --> Set are functors and t_{a,b} : F^*(a) x F_*(b) --> A(a,b) is a family natural in a and b in A. The morphisms are as you described. There is a "double Yoneda" A --> E(A) taking c to (A(c,-), A(-,c), composition). ==Ross On 06/03/2009, at 7:19 PM, Andrew Stacey wrote:
When you say that you call it 'the Isbell envelope', what do you mean? Is the category the 'Isbell envelope of/on the original category' or are the objects 'Isbell envelopes' and we have the category of Isbell envelopes (in/ on/of the original category)?