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Topic: Functorial

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	[No title]
		The most widely known model category without functorial factorizations is the category of pro-spaces or, more generally, of pro-objects (in the sense of Grot* hen- dieck) in a proper model category C [11, 19] and its Bousfield localization mod *elling the 'etale homotopy theory [4, 17].
		Then there is a functorial factorization (fl, ffi) on C such that, for all morp* *hisms f in C, the map fl(f) is in I-cof and the map ffi(f) is in I-inj.
		Appendix A. An explicit construction of a functorial fibrant replacement in pro-C The purpose of this appendix is to give an explicit construction of functorial fibrant replacements in the strict model category on pro-C. More precisely, the purpose is to prove that the construction of fibrant replacements in [19] is fu* *nctorial.
	hopf.math.purdue.edu /ChornyB/prospaces.txt (3029 words)

	Functor - Wikipedia, the free encyclopedia
		In the category of topological spaces (without distinguished point), one considers homotopy classes of generic curves, but they cannot be composed unless they share an endpoint.
		Thus one has the fundamental groupoid instead of the fundamental group, and this construction is functorial.
		Algebra of continuous functions: a contravariant functor from the category of topological spaces (with continuous maps as morphisms) to the category of real associative algebras is given by assigning to every topological space X the algebra C(X) of all real-valued continuous functions on that space.
	en.wikipedia.org /wiki/Functor (1623 words)

	[No title]
		Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists.
		This definition is functorial since factorizations in the injective model structure on Ar C are functorial.
		Since the fibrant obstruction theory for i is functorial, the obstructions for f and g are the compositions of ff with the two maps F I! Therefore, the obstructions for f and g are equal.
	jdc.math.uwo.ca /papers/obstruction.txt (7257 words)

	Chronological list of publications
		Functorial Semantics of Algebraic Theories, Proceedings of the National Academy of Science 50, No. 5 (November 1963), 869-872.
		Functorial Semantics of Elementary Theories, Journal of Symbolic Logic, Abstract, Vol.
		Functorial Concepts of Complexity for Finite Automata, (in honor of Aurelio Carboni's 60th Birthday) to appear in Theory and Applications of Categories (electronic).
	www.acsu.buffalo.edu /~wlawvere/list.html (1136 words)

	Functorial Kripke-Beth-Joyal models of the lambda Pi-calculus II: the LF logical framework (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		Functorial Kripke-Beth-Joyal models of the lambda Pi-calculus II: the LF logical framework (ResearchIndex)
		Functorial Kripke-Beth-Joyal models of the lambda Pi-calculus II: the LF logical framework (2001)
		0.3: Functorial Semantics for Multi-algebras - Corradini, Gadducci (1998)
	citeseer.ist.psu.edu /384277.html (293 words)

	Semantics of parameterised modules using sketches (Site not responding. Last check: 2007-11-03)
		One is the Cartesian closed sketch, which is an instance of the general theory of sketches introduced by Kinoshita, Power and Takeyama.
		Further research topics in this functorial approach to specification semantics would be to formulate the sharing of modules and the distinction between Sigma-algebras and (Sigma,AX)-algebras.
		In the usual universal algebraic approach, those algebraic structures without any axiomatic constraints (Sigma-algebras) play an important special role, but it is currently not obvious how to distinguish those structures from others in our functorial approach using sketches.
	homepages.inf.ed.ac.uk /dts/grants/kinoshita.html (250 words)

	WADT'99: 66 (Corradini, Gadducci) (Site not responding. Last check: 2007-11-03)
		The gs-monoidal theory is easily obtained by weakening the cartesian structure of the standard algebraic (Lawvere) theory, more precisely, by dropping the assumption of naturality of two transformations: the "duplicator" and the "discharger".
		Intuitively, in the case of algebras the arrows of the algebraic theory are one-to-one with (tuples of) terms, which are the standard way to denote derived operators of an algebra.
		Building on this intuition, we will discuss the expressive power of equational specifications of multialgebras, where an equation is a pair of term graphs, and we will compare it with other specification techniques for multialgebras proposed in the literature [4].
	www-lsr.imag.fr /WADT99/Abstracts/66.html (343 words)

	Functorial Concurrent Semantics for Petri Nets with Read and Inhibitor Arcs (Site not responding. Last check: 2007-11-03)
		We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets.
		Along the lines of the seminal work of Winskel on safe nets, the truly concurrent semantics is given at a categorical level via a chain of functors leading from the category SW-IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains.
		As an intermediate semantic model, we introduce inhibitor event structures, an extension of prime event structures able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs.
	www.di.unipi.it /~baldan/Papers/Abstract/Inibitori.html (155 words)

	Reduction of points in the group of components, by Dino J. Lorenzini (Site not responding. Last check: 2007-11-03)
		The author introduced earlier two functorial filtrations of the prime-to-$p$ part of the group of component $\Phi_K$ of ${\cal A}_K/{\cal O}_K$.
		An example of a functorial subgroup of $\Phi_K$ occuring in one of the filtrations is the group $\Psi_{K,L}$, the kernel of the natural map $\Phi_K \longrightarrow \Phi_L $, where $L/K$ denotes the minimal extension of $K$ such that $A_L/L$ has semistable reduction.
		We also discuss cases where the image of $P-Q$ belongs to a functorial subgroup of $\Psi_{K,L}$, using a pairing associated to $\Phi_K$.
	www.math.uiuc.edu /Algebraic-Number-Theory/0173 (320 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Recall that the functorial reactive system F : “ CIxt CIxt is really a family with varying choices of control signature K and of reaction rules Reacts.
		A framework is often deficient for two reasons: (i) it provides insu#cient benefits to compensate for the e#ort of casting a specific example in the framework's form; (ii) it is not rich enough to cover all the phenomena that one wants.
		I started with reactive systems, then passed to functorial reactive systems when it became clear that RPOs needed to be calculated in a separate category, then considered functorial monoidal reactive system to cater explicitly for RPOs resulting in multihole contexts.
	para.inria.fr /~leifer/articles/leifer-synlt2.txt (12814 words)

	Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics) -- Books (Site not responding. Last check: 2007-11-03)
		He focuses on the functorial and special case methods of computing asymptotic heat trace and heat content coefficients in the heat equation, and introduces results from the Seeley calculus and other methods.
		The formulas he presents can be applied in such areas as index theory, compactness theorems for moduli spaces of isospectral metrics, and zeta function regularization.
		The author focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation and introduces results derived from the Seeley Calculus and other methods.
	cadgate.com /book/un/1584883588 (296 words)

	categories: Re: Functorial injective hulls (Site not responding. Last check: 2007-11-03)
		Bill's question concerning minimal functorial injective extensions seems very interesting.
		Bill's comment was: > But by contrast, functorial injective resolutions do exist, usually > by some sort of double-dualisation monad.
		Prev by thread: categories: Re: Functorial injective hulls
	north.ecc.edu /alsani/ct99-00(8-12)/msg00144.html (159 words)

	Citations: Functorial theory of parameterized specifications in a general specification framework - Ehrig, ... (Site not responding. Last check: 2007-11-03)
		Functorial theory of parameterized specifications in a general specification framework.
		Following the idea first proposed in [13] we attempt here to work with theories as first class citizens, relegating formulae to mere presentation tools, while bringing in computability requirements.
		Moreover [240] covers the abstract investigation of module specifications in arbitrary specification frames, including an extended instantiation by the behavior specification frame.
	citeseer.lcs.mit.edu /context/156899/0 (1290 words)

	Citebase - Functorial prolongations of some functional bundles (Site not responding. Last check: 2007-11-03)
		We discuss two kinds of functorial prolongations of the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base.
		We study the prolongation of vector fields in both cases and we prove that the bracket is preserved.
		FUNCTORIAL PROLONGATIONS OF SOME FUNCTIONAL BUNDLES 11[15] Kriegl A., Michor P.W., The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs 53, AMS, 1997.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0407319 (546 words)

	[No title]
		The el* liptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology * theory on the compactification of an S1-representation is given by the sheaf cohomology* * of a suitable line bundle on the curve.
		It is also functorial for certain isogenies as explain* *ed in 4.3.
		In this section we show they are special cases of a general functorial co* nstruction of a cohomology theory EGT(.) associated to a one dimensional affine group scheme* * G. This will serve to illustrate the algebraic categories described in Section 3 and al* *so complete the motivation of our construction for elliptic curves.
	hopf.math.purdue.edu /Greenlees-Hopkins-Rosu/ellT.txt (8922 words)

	Amazon.co.uk: Functorial Knot Theory: Categories of Tangles, Coherence, Categorical Deformations, and Topological ... (Site not responding. Last check: 2007-11-03)
		Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized.
		The rich categorical structure naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.
		This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology.
	www.amazon.co.uk /exec/obidos/ASIN/9810244436 (456 words)

	International Journal of Mathematics and Mathematical Sciences (Site not responding. Last check: 2007-11-03)
		Given a measureable transformation between measure spaces, we determine when such gives rise to a mapping between the corresponding lattice of function semi-norms.
		We further determine when this mappings preserves norms and observe that it does preserve certain other important properties.
		We next establish a functorial connection between measure spaces and lattice.
	www.hindawi.com /journals/ijmms/volume-9/S0161171286000029.html (113 words)

	Pre-nets, read arcs and unfolding: a functorial presentation (Site not responding. Last check: 2007-11-03)
		Pre-nets have been recently proposed as a means of providing a functorial algebraic semantics to Petri nets (possibly with read arcs), overcoming some previously unsolved subtleties of the classical model.
		Here we develop a functorial semantics for pre-nets following a sibling classical approach based on an unfolding construction.
		Any pre-net is mapped to an acyclic branching net, representing its behaviour, then to a prime event structure and finally to a finitary prime algebraic domain.
	www.dsi.unive.it /~baldan/Papers/Abstract/pre-nets.html (148 words)

	Ph.D. DEFENSE
		But, of course, one might as well define the dimensions in terms of the derived functors and then prove that they can be interpreted in terms of resolutions.
		Functorial dimensions are defined in terms of derived functors and, in general, not expected to be interpreted in terms of resolutions.
		Some of these dimensions can, actually, be interpreted in terms of resolutions; I will write out the addition formula for these special cases to recover - with ease - a couple of formulas from the literature.
	www.math.ku.dk /cal/events/659.htm (147 words)

	AMCA: The Construction of Functorial Transitive Quasi-Uniformities by Zaid Kimmie (Site not responding. Last check: 2007-11-03)
		We examine a simplified method of constructing functorial transitive quasi-uniformities on topological spaces.
		As a consequence, we obtain spanning classes for several well-known sections of the forgetful functor from the category of Quasi-Uniform spaces to the category of Topological spaces.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/a/h/53.htm (111 words)

	Functoriality of Monotonicity Witnesses in the System of Positive (Interleaved) Inductive Types (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		We also find in [2] the notion of initial ffae-algebra as opposed to weakly initial algebra which is modelled by fi-equality.
		We now extend functoriality to any map ffae in the system M2LJ.
		For this to be true we have to add the canonical j-rule for ffae but also the conditional equality expressing (full) initiality of ffae, i.e.
	citeseer.csail.mit.edu /252663.html (264 words)

	[No title]
		The question may be whether we can choose \phi to be a functorial homotopy equivalence restricting to the particular case \Omega S^3.
		By using total Hopf invariants, there seems a chance to have the functorial version of \phi by consider the canonical retraction from \Omega\Sigma G to \Omega \Sigma (G\smash G), as I menstioned in the previous message.
		In the sense of Boardman-Steer, is the group of functorial self equivalences allowed to act on the Hopf invariants?
	www.lehigh.edu /~dmd1/wj219.txt (761 words)

	Barry Jay's Research Interests: Shape Theory
		For example, Functorial ML supports a class of functors used to support new forms of polymorphism, which go by the name of functorial or shape polymorphism, or polytypy.
		Also, FISh is an Algol-like language that supports data types of arrays, by having a distinct class of shape types.
		Functorial ML or FML written by us with Gianna Belle.
	www-staff.it.uts.edu.au /~cbj/Publications/shapes.html (1487 words)

	Caml Weekly News
		This in turn requires to allow for a user-defined order: assume sets as keys that are implemented by unordered lists.
		In this case, except for some possible efficiency issues, it seems clear that a non-functorial map is preferable, for simplicity and ease-of-use issues, and performance aside, I can't see much to recommend the current functorial approach.
		Functors would be a lot more useful if they could be used as a large-scale structural tool.
	pauillac.inria.fr /~aschmitt/cwn/2003.11.11.html (948 words)

	Computer Algebra (Site not responding. Last check: 2007-11-03)
		This substrate has a functorial architecture that has been implemented using object oriented programming techniques.
		The functorial organization allows one to define algebraic structures over arbitrary algebraic domains.
		This approach permits algebraic structures like groups, rings and fields to be first class objects that can be manipulated by the user.
	www.cs.cornell.edu /rz/computer-algebra.html (270 words)

	[No title]
		As >>you know, these are very different things, and the latter is but a >>poor substitute for the former - but hey, I never promised you that >>quantization was straightforward.
		Hmm, I haven't thought about that much, but I do recall endless arguments on sci.math about whether the algebraic completion of the rationals is a subset of the complex numbers or not.
		If there's an embedding of the algebraic completion of the rationals into the complex numbers, but no canonical one, one is abusing language to argue about whether it "IS" a subset - one should say it "can be made" into a subset.
	www.math.niu.edu /~rusin/known-math/00_incoming/phew (2022 words)

	Publications TFS 1994
		Functorial Semantics for Safe Graph Grammars Using Prime Algebraic Domains and Event Structures.
		Moreover, an axiomatic treatment of restriction is presented which allows to study in addition to refinement also implementations of parameterized specifications including restrictions.
		Finally we present an axiomatic framework for functorial semantics which opens the way to apply the theory not only to initial semantics but also to other kinds of functorial semantics, including final and specific kinds of loose semantics.
	tfs.cs.tu-berlin.de /publikationen/public1994.html (5802 words)

	The Universal Functorial Lefschetz Invariant, by Wolfgang Lueck (Site not responding. Last check: 2007-11-03)
		The Universal Functorial Lefschetz Invariant, by Wolfgang Lueck
		We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules.
		It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L^2-torsion of mapping tori.
	www.mathematik.uni-osnabrueck.de /K-theory/0235 (59 words)

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