What do I call a generalization of a fork?

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In Category Theory, we call a fork a diagram



$$Xxrightarrow;e;Abeginarrayc
xrightarrow;f;\
xrightarrow[;g;]
endarrayB$$



that commutes, i.e. $f circ e = g circ e$.



  1. In this context, what can we call $e$? Is there a proper name for it? I know it is not necessarily an equalizer of $f$ and $g$.



  2. What would I call a generalization of this concept in the following sense: given objects $A$ and $B$, a non-empty subset $H subseteq Hom(A,B)$ and a morphism $e : X rightarrow A$, we have that



    $$forall f,, g, in H., f circ e = g circ e$$



In particular, I am interested in the case where $H$ is the set of isomorphisms between $A$ and $B$.




category-theory terminology




share|cite|improve this question

















  • 2




    2. I would call it an $H$-pronged fork.
    – Qiaochu Yuan
    Jul 20 at 0:06










  • (Can't help saying "spork". Sorry...)
    – paul garrett
    Jul 20 at 0:12










  • @MaliceVidrine Yes, thanks. I fixed the question.
    – jrmn
    Jul 20 at 0:18










  • I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
    – Arnaud D.
    Jul 20 at 9:36






  • 1




    1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
    – Luca Bressan
    Jul 20 at 14:10














up vote
2
down vote

favorite
1












In Category Theory, we call a fork a diagram



$$Xxrightarrow;e;Abeginarrayc
xrightarrow;f;\
xrightarrow[;g;]
endarrayB$$



that commutes, i.e. $f circ e = g circ e$.



  1. In this context, what can we call $e$? Is there a proper name for it? I know it is not necessarily an equalizer of $f$ and $g$.



  2. What would I call a generalization of this concept in the following sense: given objects $A$ and $B$, a non-empty subset $H subseteq Hom(A,B)$ and a morphism $e : X rightarrow A$, we have that



    $$forall f,, g, in H., f circ e = g circ e$$



In particular, I am interested in the case where $H$ is the set of isomorphisms between $A$ and $B$.




category-theory terminology




share|cite|improve this question

















  • 2




    2. I would call it an $H$-pronged fork.
    – Qiaochu Yuan
    Jul 20 at 0:06










  • (Can't help saying "spork". Sorry...)
    – paul garrett
    Jul 20 at 0:12










  • @MaliceVidrine Yes, thanks. I fixed the question.
    – jrmn
    Jul 20 at 0:18










  • I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
    – Arnaud D.
    Jul 20 at 9:36






  • 1




    1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
    – Luca Bressan
    Jul 20 at 14:10












up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





In Category Theory, we call a fork a diagram



$$Xxrightarrow;e;Abeginarrayc
xrightarrow;f;\
xrightarrow[;g;]
endarrayB$$



that commutes, i.e. $f circ e = g circ e$.



  1. In this context, what can we call $e$? Is there a proper name for it? I know it is not necessarily an equalizer of $f$ and $g$.



  2. What would I call a generalization of this concept in the following sense: given objects $A$ and $B$, a non-empty subset $H subseteq Hom(A,B)$ and a morphism $e : X rightarrow A$, we have that



    $$forall f,, g, in H., f circ e = g circ e$$



In particular, I am interested in the case where $H$ is the set of isomorphisms between $A$ and $B$.




category-theory terminology




share|cite|improve this question













In Category Theory, we call a fork a diagram



$$Xxrightarrow;e;Abeginarrayc
xrightarrow;f;\
xrightarrow[;g;]
endarrayB$$



that commutes, i.e. $f circ e = g circ e$.



  1. In this context, what can we call $e$? Is there a proper name for it? I know it is not necessarily an equalizer of $f$ and $g$.



  2. What would I call a generalization of this concept in the following sense: given objects $A$ and $B$, a non-empty subset $H subseteq Hom(A,B)$ and a morphism $e : X rightarrow A$, we have that



    $$forall f,, g, in H., f circ e = g circ e$$



In particular, I am interested in the case where $H$ is the set of isomorphisms between $A$ and $B$.





category-theory terminology





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 20 at 9:33









Arnaud D.

14.7k52141




14.7k52141









asked Jul 19 at 23:50









jrmn

1113




1113







  • 2




    2. I would call it an $H$-pronged fork.
    – Qiaochu Yuan
    Jul 20 at 0:06










  • (Can't help saying "spork". Sorry...)
    – paul garrett
    Jul 20 at 0:12










  • @MaliceVidrine Yes, thanks. I fixed the question.
    – jrmn
    Jul 20 at 0:18










  • I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
    – Arnaud D.
    Jul 20 at 9:36






  • 1




    1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
    – Luca Bressan
    Jul 20 at 14:10












  • 2




    2. I would call it an $H$-pronged fork.
    – Qiaochu Yuan
    Jul 20 at 0:06










  • (Can't help saying "spork". Sorry...)
    – paul garrett
    Jul 20 at 0:12










  • @MaliceVidrine Yes, thanks. I fixed the question.
    – jrmn
    Jul 20 at 0:18










  • I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
    – Arnaud D.
    Jul 20 at 9:36






  • 1




    1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
    – Luca Bressan
    Jul 20 at 14:10







2




2




2. I would call it an $H$-pronged fork.
– Qiaochu Yuan
Jul 20 at 0:06




2. I would call it an $H$-pronged fork.
– Qiaochu Yuan
Jul 20 at 0:06












(Can't help saying "spork". Sorry...)
– paul garrett
Jul 20 at 0:12




(Can't help saying "spork". Sorry...)
– paul garrett
Jul 20 at 0:12












@MaliceVidrine Yes, thanks. I fixed the question.
– jrmn
Jul 20 at 0:18




@MaliceVidrine Yes, thanks. I fixed the question.
– jrmn
Jul 20 at 0:18












I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
– Arnaud D.
Jul 20 at 9:36




I took the liberty of removing your edit notice, as I found it confusing. Besides, if someone wants to see all the versions of the question, they can just click on the "edited [time] ago".
– Arnaud D.
Jul 20 at 9:36




1




1




1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
– Luca Bressan
Jul 20 at 14:10




1. Though it may be pushing the cutlery metaphor too far, I would call it a handle.
– Luca Bressan
Jul 20 at 14:10















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