## Category theory: proceedings of the international conference held in Como, Italy, July 22-28, 1990Aurelio Carboni, Maria Cristina Pedicchio, Giuseppe Rosolini |

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### Contents

F W LAWVERE Some thoughts on the future of category theory p | 1 |

J ADAMEK J ROSICKY What are locally generated categories? p | 14 |

J BENABOU Some remarks on free monoids in a topos p | 20 |

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2-category abelian adjunction algebra arrow axiom bialgebra bijection braiding canonical cartesian coalgebra cocomplete codomain cofibration colimits commutative comodule compact composite condition construction coproducts Corollary corresponding defined definition denote distributive categories domain replacement domF domG E-subsets element Endv(X epimorphisms equal equations equivalence of categories example factorization fibration finite dimensional forgetful functor function functor G-torsor Galois given graph groupoid Hausdorff hence homomorphism induced initial algebra injective internal inverse isomorphism kernel labelled lambda left adjoint Lemma locally Math modular monadic monoid monomorphisms morphism n-cell n-pasting scheme n+l)-cell n+l)-pasting scheme natural numbers natural transformation pair poset preframe preserves Proof Proposition prove pullback pushout quotient map relation representation result rewrite rules satisfies Section semilattice simplicial square strong stack structure subobject subsets surjective T-algebra tensor category tensor product terminal object Theorem theory topological topos trivial unique vector space weak equivalence Yang-Baxter operator