-
category theory, a
posetal category, or thin category, is a
category whose homsets each
contain at most one morphism. As such, a
posetal category amounts...
- if it is cocomplete. A
small complete category is
necessarily thin. A
posetal category vacuously has all
equalizers and coequalizers,
whence it is (finitely)...
-
trivially hold
because any
equation of
parallel morphisms is true in a
posetal category). With this 2-category structure, a
pseudofunctor F from a category...
- {\displaystyle (y,z)\circ (x,y)=(x,z).} Such
categories are
sometimes called posetal.
Posets are
equivalent to one
another if and only if they are isomorphic...
-
FinVect with a
pregroup seen as a
posetal category. This
approach has some shortcomings: all
parallel arrows of a
posetal category are equal,
which means...
-
considering the
category of open sets on X {\displaystyle X} to be the
posetal category O ( X ) {\displaystyle O(X)}
whose objects are the open sets of...
- non-negative real
numbers [ 0 , ∞ ) {\displaystyle [0,\infty )} are
viewed as a
posetal category via the ≤ {\displaystyle \leq } relation, then the Vietoris–Rips...
- {S}}}(-):\mathbb {N} ^{\operatorname {op} }\to \mathbf {Simp} } from the
opposite posetal category N op {\displaystyle \mathbb {N} ^{\operatorname {op} }} to the...
