- J{\displaystyle J} is
cofiltered if the
opposite category Jop{\displaystyle J^{\mathrm {op} }} is filtered. In detail, a
category is
cofiltered when it is not...
- as
limits of
certain functors and are
closely related to
limits over
cofiltered categories. In the literature, one
finds the
terms "directed limit", "direct...
- the
filtered colimit. AB6*) A
satisfies AB3*), and
given a
family of
cofiltered categories I j , j ∈ J {\displaystyle I_{j},j\in J} and maps A j : I j...
-
universal property. In
categorical terms, this is a
special case of a
cofiltered limit construction. A
profinite group is a compact, and
totally disconnected...
- equivalently,
functors F : I → C {\displaystyle F:I\to C} from a
small cofiltered category I.
While Pro(C)
exists for any
category C,
several special cases...
- HR(X){\displaystyle HR(X)} of
hypercoverings modulo simplicial homotopy is
cofiltering, and thus
gives a pro-object in the
homotopy category of
simplicial sets...
