## Arrows, structures, and functors: the categorical imperative |

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### Contents

Basic Concepts of Category Theory | 24 |

Monoids and Groups | 51 |

Metric and Topological Spaces | 60 |

2 other sections not shown

### Common terms and phrases

abelian monoid Abm-structure admissible algebra arbitrary arrows axioms bijection C-structure called category of sets category theory Chapter codomain coequalizer cofree colimit commutative diagram composition consider construction coproduct defined DEFINITION denote disjoint union dual dynamorphism element epimorphism equalizers equivalence relation example exercise exists a unique finite forgetful functor function given Hint identity image factorization system implies inverse isomorphism left adjoint linear maps Lipschitz maps Metl metric spaces minimal realization monad monoid homomorphism monoidal category monomorphism morphism natural transformation OBSERVATION one-to-one optimal order-preserving pair phism poset preserves products proof PROPOSITION Prove pullback q in Q Q X X0 QXX0 reachability reader respect to G right adjoint satisfies Section sequential machines Setop sets with structure Show solution set subset subspace T-algebra topological spaces topology V-category Vect vector space Verify