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I think these diagrams move me in the right direction. The idea is to transform a "limit" situation into a "colimit" situation.
upd. T needs to be a separate category with functors going into it from the SH category.
H <- R - > S
f: S -> p
g:H -> u
h: S->H
j: H ->S
S -> X
R -> X
upd. T needs to be a separate category with functors going into it from the SH category.
H <- R - > S
f: S -> p
g:H -> u
h: S->H
j: H ->S
S -> X
R -> X