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### Contents

Looking at the woods rather than the trees | 1 |

Particular objects and morphisms | 10 |

Universal constructions | 24 |

Copyright | |

7 other sections not shown

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### Common terms and phrases

abelian category additive associated bifunctor binormal category biproducts called cancellable clear clearly coker f cokernel commutative diagram complete composition Consequently consider Consider the diagram consisting coproducts deduce define Definition denote described dual element epic equaliser equivalent exact exact sequence Example Exercise exists f is epic f is monic fact factorisable faithful finite products follows functor F given gives group morphism hence identity induced initial object injective isomorphism ker coker kernel of f mapping monic Morc(A morphism f natural transformation normal Note notion observe obtain ordered set pair preserves projective Proof Prove pullback R-module represented residuated result retraction Ring RMod semi-additive semigroup Similarly simply spaces splits square statements suffices Suppose surjective terminal object Theorem unique morphism whence zero object