added (here) statement of two little lemmas relating coequalizers to kernel pairs

]]>added missing link back to *regular epimorphism*

added pointer to:

- Francis Borceux, Section 2.4 in Vol. 1:
*Basic Category Theory*of:*Handbook of Categorical Algebra*, Encyclopedia of Mathematics and its Applications**50**Cambridge University Press (1994) (doi:10.1017/CBO9780511525858)

Added this:

Coequalizers were defined in the paper

- {#EH} Beno Eckmann, Peter J. Hilton,
*Group-like structures in general categories II. Equalizers, limits, lengths*. Mathematische Annalen 151:2 (1963), 150–186. doi:10.1007/bf01344176.

for any finite collection of parallel morphisms.
The paper refers to them as *right equalizers*, whereas equalizers are referred to as *left equalizers*.

I agree. It should read to say, “$p$ is the coequalizer of the maps $f, g$”. Edit: I made an adjustment there, and also changed the word “projection” to “quotient” since projection is given the specific meaning having to do with products.

]]>Something is wrong with the terminology in the idea section.

the projection function $p \colon Y \longrightarrow Y/_\sim$ satisfies

$p \circ f = p \circ g$and in fact $p$ is universal with this property, hence it “co-equalizes” $f$ and $g$.

In the standard terminology, one says that $p$ **coequalizes** a parallel pair $f,g$ if $p\circ f = p\circ g$, period. No universality. (Co)equalizing is the same as making a (co)cone here, not the same as being a (co)equalizer/universal (co)cone !

I have added to *coequalizer* basic statements about its relation to pushouts.

In the course of this I brought the whole entry into better shape.

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