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Topic: Image (category theory)

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	The Possibility of Minimal Units in the Filmic Image by Sophie De Grauwe
		Categories and definitions have vague boundaries, which ensures their flexibility, and they are structured by salient central elements (elements which have a lot of weight in the definition or category) and weak peripheral elements (elements which are marginal in the definition or category).
		The modality of an image is determined on the basis of several modality markers, like colour saturation, contextualization (the degree of presence or absence of background), camera mobility, etc. The "truth" which is presented in images is not absolute, it is the truth of a social group.
		For example, the interpretation of an image in which a character points a gun at another character as being an instance of the syntagmatic combination (Actor-process-Goal) is only possible through the association of the characters and the process (and the relation between them) with similar characters and processes and the relations between these.
	www.imageandnarrative.be /mediumtheory/sofiedegrauwe.htm (8268 words)

	Image (category theory) - Wikipedia, the free encyclopedia
		in C, the image of f is a monomorphism
		The image of f is often denoted by im f or Im(f).
		In many concrete categories such as groups, abelian groups and (left- or right) modules, the image of a morphism is the image of the correspondent morphism in the category of sets.
	en.wikipedia.org /wiki/Image_(category_theory) (177 words)

	Como Category Theory News
		Part of the perception that category theory is "foundations" (in the pejorative sense of being remote from applications and development) is due to a preoccupation with huge size.
		The category S is itself cartesian closed, and the categories of structures of geometry and analysis are enriched in it.
		While the Fregean image involves rigid inclusion and elementhood relations imagined to be given once and for all for mathematics as a whole, the usual mathematical practice instead considers inclusion and membership relations for subsets of a given universe of discourse (such as R^3).
	categorytheorynews.blogspot.com (4364 words)

	Category Theory (Stanford Encyclopedia of Philosophy/Winter 2002 Edition)
		Category theory is a general mathematical theory of structures and sytems of structures.
		Category theory reveals that many of these constructions are in fact special cases of objects in a category with what is called a "universal property".
		Given these simple facts, it remains to be seen whether category theory should be "on the same plane", so to speak, with set theory, whether it should be considered seriously as providing a foundational alternative to set theory or whether it is foundational in a different sense altogether.
	www.science.uva.nl /~seop/archives/win2002/entries/category-theory (3063 words)

	Category Theory (Stanford Encyclopedia of Philosophy)
		Category theory is both an interesting object of philosophical study, and a potentially powerful formal tool for philosophical investigations of concepts such as space, system, and even truth.
		Category theory is, in this sense, the legitimate heir of the Dedekind-Hilbert-Noether-Bourbaki tradition, with its emphasis on the axiomatic method and algebraic structures.
		From the foregoing disussion, it should be obvious that category theory and categorical logic ought to have an impact on almost all issues arising in philosophy of logic: from the nature of identity criteria to the question of alternative logics, category theory always sheds a new light on these topics.
	plato.stanford.edu /entries/category-theory (11769 words)

	Springer Online Reference Works
		Not every category is concrete; for example, the category with as objects all topological spaces and whose morphisms are defined to be homotopy classes of continuous mappings [10].
		It follows from the definition that each object in a category has a unique identity morphism; thus it is possible to identify objects with their identity morphisms, leading to an axiomatization of categories in which  "morphism" ; and "composite" are the only primitive notions (see [9]).
		In these areas of category theory coherence theorems play an important part: these are theorems which allow one to deduce the commutativity of a large class of diagrams from that of certain particular diagrams (see [a19], for example).
	eom.springer.de /c/c020740.htm (2903 words)

	The Reference Frame: Category theory and physics
		String theory is first of all a physical theory, and it should be studied because of physical motivations - the primary physical motivation is to locate the right ideas and equations that describe the real world.
		Category theory has been used by many to achieve completely wrong physical conclusions - for example, by considering the "pompously foolish" quantization functor, many people have claimed that everything that happens in a classical theory has a counterpart in the "corresponding" quantum theory.
		Category theory often resembles linguistics (or even postmodern literary criticism): it is a science about arrows between different objects and about creating new objects from these arrows, but it does not really care too much whether the objects exist and what are their real properties.
	motls.blogspot.com /2004/11/category-theory-and-physics.html (3683 words)

	IRM: Integrated Region Matching for Image Retrieval
		The query image in Figure 5 is difficult to match because objects in the image are not distinctive from the background.
		For each of the 9 image categories, the average precision and weighted precision based on the 3 sample images are plotted in Figure 6.
		The image category identification number is assigned according to Table 1 scanned row wise.
	www-db.stanford.edu /IMAGE/Simplicity/ACM00.1/li (5394 words)

	Category Theory (Site not responding. Last check: 2007-10-08)
		Category theory looks at mathematics on a large scale: objects and the relations between them, in the abstract.
		An informal survey of such connections is "Topology and higher-dimensional category theory: the rough idea".
		On the geometric side, he has studied relationships between n-categories and cubes; see Multiple categories: the equivalence of a globular and a cubical approach (with F. Al-Agl and R. Brown), Advances in Mathematics 170 (2002), 71-118.
	www.maths.gla.ac.uk /research/groups/categoryth (425 words)

	MATHS: Category Theory
		Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic.
		A Category is a mixture of an algebra and a directed graph.
		Category theory shows that in most known algebras and logistic systems, there is a way to construct an equivalent.
	www.csci.csusb.edu /dick/maths/math_25_Categories.html (3607 words)

	Image and Narrative Issue 6. Medium Theory
		Both definitions are considered and problematized from a theoretical and a practical point of view and a compromise is proposed in which their inextricable nature is underlined.
		For narratologists then, medium as a category is significant to the extent that the choice of a certain medium, e.g.
		It is an attempt to construct a medium theory that remains true to George Spencer-Brown’s logical calculus on the one hand, and that gives full “credit” to Niklas Luhmann’s considerations on the medium/form distinction on the other hand.
	www.imageandnarrative.be /mediumtheory/mediumtheory.htm (2176 words)

	Inverse Image Category (Preimage Category)
		, is mainly terminological note to be used as a base of my other category theory articles.
		on the inverse image category should be normally clear from the context (e.g.
		So essentially inverse image maps a partially ordered category to a partially ordered category.
	www.mathematics21.org /categories/inverse-image.xml (376 words)

	The Math Forum - Math Library - Number Theory
		Papers from a Mathematics graduate from The University Of Sussex at Brighton: Number Theory: GCD and Prime Factorisation; Molien's Theorem, Invariant Theory and Gregor Kemper; A History of Equality.
		In number theory, straightforward, reasonable questions are remarkably easy to ask, yet many of these questions are surprisingly difficult or even impossible to answer.
		A connected series of four problems in elementary number theory that are ideal for discovery learning at several levels.
	mathforum.org /library/topics/number_theory (2144 words)

	Category Theory Applied to Neural Modeling and Graphical Representations - Healy (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Category Theory Applied to Neural Modeling and Graphical Representations (2000)
		Abstract: Category theory can be applied to mathematically model the semantics of cognitive neural systems.
		1 Introduction In this paper, we describe a mathematical scheme for the analysis and design of cognitive neural network architectures based upon functors and natural transformations, the structural mappings of category theory.
	citeseer.ist.psu.edu /healy00category.html (338 words)

	week73
		A category is something just as abstract as a set, but a bit more structured.
		This is true, not only because Russell's paradox tends to ruin attempts at a consistent theory of the "thing of all things", but because, just as what really counts is the category of all sets, what really counts is the 2-category of all categories.
		So the category of all sets is "one-dimensional": it has both objects or "dots" and morphisms or "arrows between dots".
	math.ucr.edu /home/baez/week73.html (2359 words)

	Amazon.com: Sampling Theory in Signal and Image Processing: Magazines (Site not responding. Last check: 2007-10-08)
		Founded in 2002, Sampling Theory in Signal and Image Processing is published three times a year, in January, May, and September.
		The intended audience includes mathematicians, scientists, and engineers interested in cutting-edge research in sampling and interpolation theory and its applications.
		Publishes research papers in sampling and interpolation theory and applications in signal and image analysis, and other related fields.
	www.amazon.com /Sampling-Theory-Signal-Image-Processing/dp/B000071HMC (434 words)

	Category Theory (Stanford Encyclopedia of Philosophy/Summer 1998 Edition)
		Category Theory (Stanford Encyclopedia of Philosophy/Summer 1998 Edition)
		Y, P(f): P(X) P(Y) takes a subset A of X and maps it to B = f(A), the image of f restricted to A in Y. It is easily verified that it is a functor.
		Hypatia (The Queen Mary and Westfield College directory of mathematicians and computer scientists)
	www.science.uva.nl /~seop/archives/sum1998/entries/category-theory (3074 words)

	theory - SWiK
		The contents of theory page and all pages directly attached to theory will be erased.
		Bunch of papers by Philip Walder on topics such as the relationship between Category Theory and Monads in Haskell.
		Programming haskell category theory paper monad … Nov 27
	swik.net /theory (627 words)

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