Category Theory II 2: Limits, Higher order functors

1.2 Introduction to Limit 

Analogy : Product to Cones (Limit)

2.1 Five categories used to define Limit:

  1. Index category (I)
  2. Category C: Functors (constant ,  D)
  3. Cones (Lim D)
  4. Functor Category [I, C ]:objects are (constant, D ), morphisms are natural transormations
  5. Set category of Hom-Set Cones [I,C] to Hom-Set C (c , Lim D )

2.2 Naturality

3.1 Examples: Equalizer

CoLimit = duality of Limit (inverted cone = co-Cone)

Functor Continuity = preserve Limit

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