Abstract
? | Restriction categories were first introduced in the early 1990s and later
studied in the early 2000s as a means of generalising the notion of a partial
map category; the idea being to capture the partiality of each map through a
corresponding idempotent on its domain, called a restriction idempotent. As it
turns out, the hom-sets of any restriction category has a natural partial
ordering, and this, together with the notion of compatibility, gave rise to the
notion of a join restriction category.
In this talk, we shall see that every join restriction category may be freely
completed to a cocomplete join restriction category, given by the partial map
category of sheaves on some site. However, we shall also see that every join
restriction category has a free cocompletion equivalent to this partial map
category of sheaves. This equivalent category takes a simpler form, with join
restriction presheaves as its objects. |
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