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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 21st 2016

    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.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 21st 2017

    Something is wrong with the terminology in the idea section.

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

    pf=pg p \circ f = p \circ g

    and in fact pp is universal with this property, hence it “co-equalizes” ff and gg.

    In the standard terminology, one says that pp coequalizes a parallel pair f,gf,g if pf=pgp\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 !

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 21st 2017
    • (edited May 21st 2017)

    I agree. It should read to say, “pp is the coequalizer of the maps f,gf, 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.

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