Category Theory: Proceedings of the International Conference Held in Como, Italy, July 22-28, 1990, Issue 1488Aurelio Carboni, Maria Cristina Pedicchio, Giuseppe Rosolini With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/Street (80 pp) on a growing subject: it gives an account of classical Tannaka duality in such a way as to be accessible to the general mathematical reader, and to provide a key for entry to more recent developments and quantum groups. No expertise in either representation theory or category theory is assumed. Topics such as the Fourier cotransform, Tannaka duality for homogeneous spaces, braided tensor categories, Yang-Baxter operators, Knot invariants and quantum groups are introduced and studies. From the Contents: P.J. Freyd: Algebraically complete categories.- J.M.E. Hyland: First steps in synthetic domain theory.- G. Janelidze, W. Tholen: How algebraic is the change-of-base functor?.- A. Joyal, R. Street: An introduction to Tannaka duality and quantum groups.- A. Joyal, M. Tierney: Strong stacks andclassifying spaces.- A. Kock: Algebras for the partial map classifier monad.- F.W. Lawvere: Intrinsic co-Heyting boundaries and the Leibniz rule in certain toposes.- S.H. Schanuel: Negative sets have Euler characteristic and dimension.- |
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 |
Copyright | |
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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 Cosk defined definition denote distributive categories domain replacement element End(V epimorphisms equal equations example factorization fibration forgetful functor Fourier function functor G-torsor Galois given graph groupoid Hausdorff hence homomorphism induced initial algebra injective internal inverse isomorphism labelled lambda left adjoint Lemma locally Math modular monadic monoid monomorphisms morphism n-cell n-pasting scheme n+1)-pasting scheme natural transformation object pair poset preframe preserves Proof Proposition prove pullback Q-sets quotient map representation result rewrite rules satisfies Section semilattice sequence simplicial square strong stack structure subcategory subobject subsets surjective T-algebra tensor category terminal object Theorem theory topological topos unique vector space weak equivalence Yang-Baxter operator λες