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Cardinal Addition in Distributive Allegories [chapter]

Yasuo Kawahara, Michael Winter
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we want to develop an addition operation on an abstract notion of cardinality of relations in a distributive allegory.  ...  Assuming suitable extra structure on the underlying allegory we are going to define addition and investigate its basic properties.  ...  Conclusion and Outlook In this paper we extended the notion of a cardinal function to distributive allegories, and we defined a suitable notion of addition of cardinal numbers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04639-1_16">doi:10.1007/978-3-642-04639-1_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z4tgx6rxxndsxjsndtazswcraq">fatcat:z4tgx6rxxndsxjsndtazswcraq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110401051257/http://www.cosc.brocku.ca/files/downloads/research/cs0904.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/db/e8/dbe85f499ed0d7e61c144f89016b1c465a8e7429.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04639-1_16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Complements in Distributive Allegories [chapter]

Michael Winter
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In particular, we will show that partial identities do have complements in distributive allegories with relational sums and total splittings assuming the axiom of choice.  ...  In particular, we will show that partial identities do have complements in distributive allegories with relational sums and total splittings assuming the axiom of choice.  ...  We will generalize this result to certain classes of relations in distributive allegories.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04639-1_23">doi:10.1007/978-3-642-04639-1_23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/axwpxhsmdbhunlacdxmarnei6a">fatcat:axwpxhsmdbhunlacdxmarnei6a</a> </span>
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Relations and Kleene algebras in computer science

Rudolf Berghammer, Bernhard Möller, Georg Struth
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anq6kvwvqbegtipq5vfhvonzqq" style="color: black;">The Journal of Logic and Algebraic Programming</a> </i> &nbsp;
In addition, it is shown that every demonic refinement algebra with enabledness is also a demonic refinement algebra with termination.  ...  It was posed by a university administration and concerns the construction of a timetable with an even distribution of certain mandatory courses.  ...  For all three variants a canonical cardinality function is shown to be initial in the category of all cardinality functions over the given allegory.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jlap.2010.07.011">doi:10.1016/j.jlap.2010.07.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lu2ocemoafcfngd5lrq7256hxy">fatcat:lu2ocemoafcfngd5lrq7256hxy</a> </span>
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Products in categories of relations

Michael Winter
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anq6kvwvqbegtipq5vfhvonzqq" style="color: black;">The Journal of Logic and Algebraic Programming</a> </i> &nbsp;
In this paper we investigate a canonical weakening of the notion of a relational product.  ...  An allegory is called a distributive allegory if (5) Notice that allegories and distributive allegories are defined by equations. The same can be done for division allegories [4] .  ...  This time we have the following cardinalities: |R[V , V ]| = 79, |R[V , U]| = 29, |R[U, U ]| = 13.In this allegory V is a weak relational product of U with itself.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jlap.2007.10.003">doi:10.1016/j.jlap.2007.10.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ad7wnuefwbaa3jd4rmo5up5zoq">fatcat:ad7wnuefwbaa3jd4rmo5up5zoq</a> </span>
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The Castle of the Body

C. L. Powell
<span title="1919-04-01">1919</span> <i title="University of North Carolina Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jdcp5bacdbe5fkqlsecu4xydw4" style="color: black;">Studies in Philology</a> </i> &nbsp;
In addition we have the introduction of the five wits and the omission of the less tangible seven virtues, although these are suggested in the various defenders of the castle from the attacks of the vices  ...  In the Vita de Dowel, Dobet and Dobest, the second part of Piers the Plowman, the same castle allegory occurs again.  ... 
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Determinisation of relational substitutions in ordered categories with domain

Wolfram Kahl
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anq6kvwvqbegtipq5vfhvonzqq" style="color: black;">The Journal of Logic and Algebraic Programming</a> </i> &nbsp;
Restating a unification problem as a single relational substitution instead of as multiple functional substitutions (or terms), a solution becomes a "determiniser" arrow and allows formalisation in the  ...  This relies on the determinacy concept of "characterisation by domain" introduced by Desharnais and Möller for Kleene algebras with domain; this is here applied in the weakest possible setting.  ...  A Kleene allegory is a distributive allegory that is also a Kleene category. A Dedekind category [29, 30] is a distributive allegory with residuals and top morphisms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jlap.2010.07.017">doi:10.1016/j.jlap.2010.07.017</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qs3h4py5t5azth2xpnskiywna4">fatcat:qs3h4py5t5azth2xpnskiywna4</a> </span>
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Political Ideas in Sienese Art: The Frescoes by Ambrogio Lorenzetti and Taddeo di Bartolo in the Palazzo Pubblico

Nicolai Rubinstein
<span title="">1958</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xbgykiazp5ajlbzvm4kzkmbfbu" style="color: black;">Journal of the Warburg and Courtauld Institutes</a> </i> &nbsp;
In the Lorenzetti fresco, the ruler is surrounded by the four cardinal virtues and Magnanimity, with Peace a little apart.'1 The specula principum placed the emphasis on the cardinal virtues; in the Lorenzetti  ...  The allegory of 'Buon Governo' thus occupies the central position among the frescoes of the Sala de' Nove.s It does so in more than one respect.  ...  In addition to three cardinal or political virtues, Justice, Prudence and Fortitude, we again find Magnanimity (P1. I7a, b, c, d); but Peace and Concord are missing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/750823">doi:10.2307/750823</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/edy5vu4jpfdrlhrm7yqsrpivs4">fatcat:edy5vu4jpfdrlhrm7yqsrpivs4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150308010131/https://www3.nd.edu/~pweithma/justice_seminar/Siena/Rubenstein%20%28Political%20Ideas%20in%20Sienese%20Art%29.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/92/96/929672baee3930c70bd14759b0a026252afe77f4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/750823"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Page 160 of The Art-Journal Vol. 5, Issue 53 [page]

<span title="">1859</span> <i title="Out-of-copyright"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_art-journal-us" style="color: black;">The Art-Journal </a> </i> &nbsp;
In these days of bright and glowing har- monies, the eye is at once strack with the virtuous abstinence from colour which the artist has made a cardinal principle in the execution of the picture.  ...  These are all of iron, and we mention them a being of a style in a oe from mytho- logy and allegory, and do not hesitate to propose that in order to avoid the humiliating errors into w we have fallen in  ... 
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Cardinal de Richelieu's discovery of purple: Political and emblematic antecedents of a topos

Maria Neklyudova, The Russian Presidential Academy of National Economy and Public Administration
<span title="">2020</span> <i title="The Russian Presidential Academy of National Economy and Public Administration"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/all76z4mqbdpblg3gyglnaumpm" style="color: black;">Shagi / Steps</a> </i> &nbsp;
cardinal de richelieu'S diScoVery of purple: poliTical and emblemaTic anTecedenTS of a TopoS Аннотация.  ...  Therefore, the allegory had to stress the dog's absolute fidelity to its master: as I suggested before, Boissière's device was intended as a message from the new cardinal to the king.  ...  had little to do with Puteanus' allegory or with its realization by von Loon and Galle.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22394/2412-9410-2020-6-4-245-275">doi:10.22394/2412-9410-2020-6-4-245-275</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pjybfdk7a5b5rne622zsdea4ry">fatcat:pjybfdk7a5b5rne622zsdea4ry</a> </span>
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Exact completions and small sheaves [article]

Michael Shulman
<span title="2012-09-05">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The theorem is that "k-ary exact categories" are a reflective sub-2-category of "k-ary sites", for any regular cardinal k.  ...  Along the way, we define a slightly generalized notion of "morphism of sites", and show that k-ary sites are equivalent to a type of "enhanced allegory".  ...  Similarly, our ω-ary allegories and K-ary allegories are called distributive and locally complete allegories, respectively, in [FS90] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1203.4318v2">arXiv:1203.4318v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uynogck3ijgddmb7qjvmuqhlea">fatcat:uynogck3ijgddmb7qjvmuqhlea</a> </span>
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RelView and Rath – Two Systems for Dealing with Relations [chapter]

Rudolf Berghammer, Gunther Schmidt, Michael Winter
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we present two systems for dealing with relations, the RelView and the Rath system.  ...  The Rath-System The Rath-System presents a library of Haskell modules that allows to explore relation algebras and several weaker structures such as categories, allegories, distributive allegories, division  ...  A next step in the hierarchy of structures could be the representation of allegories.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-24615-2_1">doi:10.1007/978-3-540-24615-2_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fqzliasyhrc2vbaff4enpvrgde">fatcat:fqzliasyhrc2vbaff4enpvrgde</a> </span>
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Art in an Age of Revolution, 1750-1800, by Albert BoimeArt in an Age of Revolution, 1750-1800, by Albert Boime. Chicago, University of Chicago Press, 1987. xxviii, 522 pp. $35.00 U.S

Pat Anderson
<span title="">1988</span> <i title="University of Toronto Press Inc. (UTPress)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3n4z4kx3sja4npv5p5nbq4b6ly" style="color: black;">Canadian Journal of History</a> </i> &nbsp;
In addition, Boime’s interest in revealing the commercial face of art leads him on occasion into the anachronistic use of terminology.  ...  Winckelmann as just one more opportunistic profiteer "in the wheeling and dealing circles of [art patron] Cardinal Albani and Company" (p. 74)?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3138/cjh.23.3.414">doi:10.3138/cjh.23.3.414</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gvsak3fyk5ebbhmw52zbglrcni">fatcat:gvsak3fyk5ebbhmw52zbglrcni</a> </span>
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Page 318 of None Vol. 7, Issue 176 [page]

<span title="1859-03-12">1859</span> <i title="Out-of-copyright"> <a target="_blank" rel="noopener" href="https://archive.org/details/None" style="color: black;">None</a> </i> &nbsp;
Second Edition, corrected and improved; with copious Additions, comprising new chapters on the Cardinals, the Inquisition, the Campagna, a Walk through a Roman Mad-house, a Visit to San Spirito with the  ...  Po the Roman Deaf and Dumb Pupils, Sketches of Schools and Asylums, Mate: Progress and Finance, the Jew-boy Mortara, the Distribution of Prizes in the Propaganda, & c.  ... 
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CHAUCER AND MORAL PHILOSOPHY: THE VIRTUOUS WOMEN OF "THE CANTERBURY TALES"

BAKER
<span title="">1991</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5uf33yyupfae7egwg5q4kpvlry" style="color: black;">Medium Ævum</a> </i> &nbsp;
on distributive justice, and Abelard, Alain de Lille and Aquinas reiterate it later in the Middle Ages. 17 The correspondence between this cardinal virtue and Griselda's behaviour becomes most apparent  ...  Chaucer's addition is intended to indicate that Virginia exemplifies this third cardinal virtue. 29 In De Inventione Cicero identifies three parts of temperance: continence, clemency and modesty. 30  ... 
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Page 447 of National Union Catalog Vol. 36, Issue [page]

<span title="1942-07-31">1942</span> <i title="J W Edwards Publisher In"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_national-union-catalog" style="color: black;">National Union Catalog </a> </i> &nbsp;
Diet te ° fl cardinal Niccold da Prato.—Nicastro, 8. Memorie e culto di Dante in Prato.—Nicastro, S. Catelogo della mostra dantesca in Roncion! settembre-novembre 1921. 1.  ...  greeter coptes, for distribut jr ¥. 2: “This edition te Iiuite!  ... 
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