category-theory-notations.typ

// Notations for category theory
#let Cat = math.bold[Cat]
$Cat$ is the category of small categories

#let CAT = math.bold[CAT]
$CAT$ is the category of small categories

#let Mon = math.bold[Mon]
$Mon$ is the category of monoids

#let Top = math.bold[Top]
$Top$ is the category of topological spaces

#let Ring = math.bold[Ring]
$Ring$ is the category of not-necessarily commutative rings.

#let Grp = math.bold[Grp]
$Grp$ is the category of groups.

#let Ab = math.bold[Ab]
$Ab$ is the category of Abelian groups.

#let colim = math.bold[colim]
$colim$ is colimit

#let WC(XX,YY) = [WeightedColimit(#XX,#YY)]

#let Psh(x) = [$bold("Psh")(#x)$]
$Psh(C)$ is the category of presheaves on $C$.
#let el = math.bold[el]
$el$ is the category of elements of a presheaf

#let Sh(x) = [$bold("Sh")(#x)$]
$Sh(X)$ is the category of sheaves on $X$.

#let Hom(cat:[],x,y) = $bold("Hom")_(cat)(#x,#y)$
The category of small categories

#let Nat(F,G) = $bold("Nat")(#F,#G)$

#let Ch(AA) = $bold("Ch")(#AA)$

#let co(ff, gg) = $ff dot gg$
#let id(C) = [$text("id")_#C$]

#let cong = math.tilde.equiv
$cong$ is contruence, isomorphism
#let Set = math.bold[Set]
$Set$ is the category of small sets
#let circ = math.circle.stroked.tiny
$circ$ is morphism composition

#let op(p) = [$#p^text("op")$]