21/07/15 23:52:42.24 0.net
For any category C and any object c ∈ C, show that:
(i) There is a category c/C whose objects are morphisms
f : c → x with domain c and in which a morphism from
f : c → x to g : c → y is a map h : x → y between the codomains
so that the triangle commutes, i.e., so that g = hf.
(ii) There is a category C/c whose objects are morphisms
f : x → c with codomain c and in which a morphism from
f : x → c to g : y → c is a map h : x → y between the domains
so that the triangle commutes, i.e., so that f = gh.
The categories c/C and C/c are called slice categories of C under and over c, respectively
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