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Universality

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Part of the Compact Textbooks in Mathematics book series (CTM)

Abstract

Let us recall the definition of a comma category (mid level of generalization). If \( G:\mathcal{D}\Rightarrow \mathcal{C} \) is a functor and \( C\in \mathcal{C} \) is an (anchor) object, then the comma category (C → G) is the category whose objects are the pairs
$$ \left(U,u:C\to GU\right) $$
for \( U\in \mathcal{D} \). Moreover, a morphism
$$ \tau :\left(U,u:C\to GU\right)\to \left(D,f:C\to GD\right) $$
between comma objects is essentially just a morphism τ: U → D in \( \mathcal{D} \) for which
$$ G\tau \circ u=f $$
(We have dropped the overbar notation \( \overline{\tau} \).)

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.California State University, FullertonIrvineUSA

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