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4639045 No.4639045 [Reply] [Original]

I have a functor <span class="math">F:C \to D [/spoiler] and all endomorphisms in the image of <span class="math">F[/spoiler] are identity morphisms. (<span class="math">F(f):F(c) \to F(c) [/spoiler] means <span class="math">F(f) [/spoiler] is identity on <span class="math">c[/spoiler])

Is there a name for such functors??

>> No.4639050

>>4639045
>functor
>endomorphisms
>morphisms

protip: just becasue they use some words in tecnobable on startrek doesnt make them real.

GTFO sci

>> No.4639091

>>4639050
0/10

>> No.4639105

So that means any <span class="math">F(f): F(a) \to F(b)[/spoiler] and <span class="math">F(g): F(b) \to F(a)[/spoiler] are isomorphisms, and the target category minus the isomorphisms has a directed underlying graph.
I think this target category may have a name, rather than the functor. I don't know the name, though.

>> No.4639132

>>4639105
Thanks, I will look into it.