Marta Bunge and Jonathon Funk, On a bicomma object condition for KZ-doctrines, J. Pure Appl. Alg. 143:69-105, 1999. Home/Search Document Not in Database Summary Related Articles Check |
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Van Kampen theorems for toposes - Bunge, Lack (1 citation) Self-citation (Bunge) (Correct)
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Marta Bunge and Jonathon Funk, On a bicomma object condition for KZ-doctrines, J. Pure Appl. Alg. 143:69-105, 1999.
The Hurwitz Action and Braid Group Orderings - Funk (2001) Self-citation (Funk) (Correct)
.... pullback stability property has a topos theory proof: a locally 0 acyclic map induces what is usually called a locally connected geometric morphism of sheaf toposes [16] The pullback stability of the pure, cosheaf factorization along a locally connected geometric morphism has been established in [5]. The projection map S I ## S is locally 0 acyclic, so that m I is a cosheaf space and # I is pure. Lifting a homeomorphism and lifting a braid are not exactly the same matter because a braid is really an isotopy equivalence class of homeomorphisms. We review this in the next section. ....
M. Bunge and J. Funk. On a bicomma object condition for KZ-doctrines. J. Pure Appl. Alg., 143:69--105, 1999.
Distribution Algebras and Duality - Bunge, Funk (2000) Self-citation (Bunge Funk) (Correct)
....0. INTRODUCTION By an S valued distribution on a topos E bounded over a base topos S it is meant here a cocontinuous S indexed functor : E S. Since introduced by F. W. Lawvere in 1983, considerable progress has been made in the study of distributions on toposes from a variety of viewpoints [19, 15, 24, 5, 6, 12, 7, 8, 9]. However, much work still remains to be done in this area. The purpose of this paper is to deepen our understanding of topos distributions by exploring a (dual) lattice theoretic notion of distribution algebra. We characterize the distribution algebras in E relative to S as the S bicomplete ....
....to be a cosheaf, but in this case one may lose the local connectedness of D over S. We remark that in those cases where D is locally connected over S, then the pair h ; di is the complete spread associated with the cosheashi cation of M . In particular, and on account of Proposition 4:9 in [9], this is the case whenever E , P(C) is an S essential geometric morphism, meaning that the (S indexed) left adjoint a a i itself has (an S indexed) left adjoint. In other words, if the topos E bounded over S admits a site presentation hC; ji for which the canonical inclusion E , P(C) is ....
M. Bunge and J. Funk, On a bicomma object condition for KZ-doctrines, J.Pure Appl.Alg. 143(1999) 69-105.
The Michael Completion of a Topos Spread - Bunge, Funk Self-citation (Bunge Funk) (Correct)
....of the strongly pure and of the weakly entire geometric morphisms de ned over a base topos S is closely connected with the possibility of giving a constructive version also of the uniqueness part in the pure entire factorization of P.T. Johnstone [14] It deserves further investigation (beyond [6]) 5. In our investigations concerning distributions, a particular role was played by the symmetric topos [2, 3, 4, 5, 6] which is a topos classi er of distributions on any S bounded topos E , equivalently, a classi er of the complete spreads over E with a locally connected domain. It would ....
....with the possibility of giving a constructive version also of the uniqueness part in the pure entire factorization of P.T.Johnstone [14] It deserves further investigation (beyond [6] 5. In our investigations concerning distributions, a particular role was played by the symmetric topos [2, 3, 4, 5, 6], which is a topos classi er of distributions on any S bounded topos E , equivalently, a classi er of the complete spreads over E with a locally connected domain. It would perhaps be interesting to investigate the question of the existence and properties of a topos classi er for the Michael ....
M. Bunge and J. Funk, On a bicomma object condition for KZ-doctrines, J. Pure Appl. Algebra 143 (1999) 69-105.
On Branched Covers In Topos Theory - Funk (2000) Self-citation (Funk) (Correct)
....subtopos as a category of fractions of branched covers, in the sense of Fox [10] of the including topos. We also have some new results concerning the general theory of KZ doctrines, such as the closure under composition of discrete fibrations for a KZ doctrine, in the sense of Bunge and Funk [6]. Introduction The notion of a branched cover is essentially due to Riemann. Since his time, branched covers have found applications in knot theory [9, 21] in the study of 3 manifolds [17] and in algebraic geometry [22] for example. A development that is of particular interest to this paper ....
....use granted. 1 Theory and Applications of Categories, Vol. 7, No. 1 2 E S C op D S D op = Figure 1: Complete spread as a display topos . able to clarify the closure of complete spreads under composition in terms of the general theory of KZ doctrines, since from [6] we know that a complete spread may be equivalently regarded as a discrete fibration for the symmetric monad [2] We shall begin in the next section with a brief introduction to complete spreads in topos theory, based on the results of [4, 5, 6] For details concerning locally connected toposes ....
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M. Bunge and J. Funk. On a bicomma object condition for KZ-doctrines. J. Pure Appl. Alg., 143:69--105, 1999.
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