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Graphbased logic and sketches I: The general framework. Available by web browser from http://www.cwru.edu/1/class/mans/math/pub/wells
, 1996
"... Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic. ..."
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Cited by 8 (4 self)
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Sketches as a method of specification of mathematical structures are an alternative to the stringbased specification employed in mathematical logic.
Sketches: Outline with References
 Dept. of Computer Science, Katholieke Universiteit Leuven
, 1994
"... This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions o ..."
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Cited by 2 (0 self)
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This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions of some of the less standard terms used in the paper, but the reader is expected to be familiar with the basic ideas of category theory. A rough machine generated index begins on page 21. I would have liked to explain the main ideas of all the papers referred to herein, but I am not familiar enough with some of them to do that. It seemed more useful to be inclusive, even if many papers were mentioned without comment. One consequence of this is that the discussions in this document often go into more detail about the papers published in North America than about those published elsewhere. The DVI file for this article is available by anonymous FTP from ftp.cwru.edu in the directory
Deducibility and Exactness
, 1998
"... What I intend to show in this short paper is how one can translate in relational terms the concepts of deducibility and exactness which are the result of a sequence of works on homology theory and algebraic topology. As we shall see, we shall obtain as a final product the possibility to associate to ..."
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What I intend to show in this short paper is how one can translate in relational terms the concepts of deducibility and exactness which are the result of a sequence of works on homology theory and algebraic topology. As we shall see, we shall obtain as a final product the possibility to associate to an arbitrary binary relation R a difunctional relation R e contained in R, in contrast with the difunctional closure of R which is larger that R. In [8] we have built from a given Ferrers relation R the relation 1 R # R # R 1 # + R and proved its difunctionality, but in fact, as already noticed by Schmidt and Strohlein ([10] p. 78 Prop. 4.4.14) R # R # R 1 # + R is difunctional even when R is arbitrary. I shall show that, in fact, R # R # R 1 # + R and R e are identical. It is important to notice that the construction used here for the definition of R e is made without using the Boolean di#erence operation. Keywords: Binary relations, homology, exact squares, r...
Accessible categories: The foundations of categorical model theory,
"... topological and geometrical structures in Banach spaces, Mem. Amer. Math. ..."
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topological and geometrical structures in Banach spaces, Mem. Amer. Math.