Is there an established name for this $eql$ function?
$$\operatorname{eql}(f, g) = \{\ (x, y)\mid f(x) = g(y)\ \}$$
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In category theory, such a set is exactly the equalizer object of the arrows $f$ and $g$ in the category of sets. – MJD May 17 '14 at 16:27
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1See this answer. – Bill Dubuque May 17 '14 at 16:31
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According to Wikipedia it's called an equalizer even outside of category theory. – MJD May 17 '14 at 16:35
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According to Wikipedia this set is called an equalizer of the two functions.
MJD
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I've discovered through Reddit (see Bill's link) that this is called the pullback:
$$pb(f, g) = \{\ (x, y) \mid f(x) = g(y)\ \}$$
The equalizer is:
$$eql(f, g) = \{\ x \mid f(x) = g(x)\ \}$$
But we can define each in terms of the other:
$$pb(f, g) = eql(f \circ \pi_1, g \circ \pi_2)$$
$$eql(f, g) = pb(f, g) \cap pb(id, id)$$
Will
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