# User:Michiexile/MATH198/Lecture 7

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## Contents |

### 1 Some adjunctions we already know

- initial/terminal are adjunctions.
- (co)-products are adjunctions.
- Actually, all (co)limits are adjunctions.

### 2 Some adjunctions we don't know yet

- Existential and universal qualifiers as adjunctions.
- Powersets and im(f) -| f^\inv

### 3 Properties of adjoints

#### 3.1 RAPL: Right Adjoints Preserve Limits

#### 3.2 Recognizing adjoints

**Theorem** (Freyd: The Adjoint Functor Theorem)