nLab
jointly monic morphisms

Contents

Contents

Definition

Given a category CC and objects a,bOb(A)a, b \in Ob(A), a pair of morphisms f,gMor(a,b)f, g \in Mor(a, b) are jointly monic if for every object c:Ob(A)c:Ob(A) and pair of morphisms h,kMor(c,a)h, k \in Mor(c, a), fh=fkf \circ h = f \circ k and gh=gkg \circ h = g \circ k imply that h=kh = k.

In a well-pointed category CC, given objects a,bOb(A)a, b \in Ob(A), a pair of morphisms f,gMor(a,b)f, g \in Mor(a, b) are jointly injective if for every global element h,kMor(1,a)h, k \in Mor(1, a), fh=fkf \circ h = f \circ k and gh=gkg \circ h = g \circ k imply that h=kh = k.

In tablular allegories

In every tabular allegory, a relation RR could be factored into jointly monic maps ff and gg such that f g=Rf^\dagger \circ g = R.

See also

References

Last revised on May 13, 2022 at 21:49:46. See the history of this page for a list of all contributions to it.