Topos8@aol.com writes:
I've been reading Lawvere's 1970 paper "Equality in hyperdoctrines and comprehension schema...." which appeared in the AMS series Symposia in Pure Mathematics, volume 17, pp 1-14.
In the first line on page 12 he refers to the " 'twisted morphism category' " B^ and the forgetful functor from B^ to (B op) x (B).
Objects of B^ are morphisms (f:a->b) of B. Morphism from (f:a->b) to (g:c->d) in B^ is a pair of morphisms ((p:c->a),(q:b->d)), forming together with f and g commuting square (note the direction of arrows). Alternatively, one can define 'twisted morphism category' as Grotendieck construction for Hom functor: Hom: B^op x B -> Set.
Can someone explain what this twisted morphism category is and/or provide a reference to the definition?
Thanks for your help.
Carl Futia
Nikita.