nLab
solution

A solution to an equation f(x)=g(x)f(x) = g(x) is a choice of value vv for the free variable xx such that the statement f(v)=g(v)f(v) = g(v) becomes true.

If we think of the equation as embodied by a pair of parallel morphisms

X 1AAAAf 2f 2X 2 X_1 \underoverset{\underset{f_2}{\longrightarrow}}{\overset{f_2}{\longrightarrow}}{\phantom{AAAA}} X_2

then a solution is a cone over this diagram. The solution space itself is the limit cone, hence the equalizer of the diagram.

Created on May 3, 2017 at 12:29:42. See the history of this page for a list of all contributions to it.