Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Coherent bicartesian and sesquicartesian categories
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 2183
First page: 78
Last page: 92
Conference: International Seminar on Proof Theory in Computer Science, PTCS 2001; Dagstuhl Castle; Germany; 7 October 2001 through 12 October 2001
Issue Date: 1-Jan-2001
Rank: M21
ISBN: 978-3-540-42752-0
ISSN: 0302-9743
DOI: 10.1007/3-540-45504-3_6
Sesquicartesian categories are categories with nonempty finite products and arbitrary finite sums, including the empty sum. Coherence is here demonstrated for sesquicartesian categories in which the first and the second projection from the product of the initial object with itself are the same. (Every bicartesian closed category, and, in particular, the category Set, is such a category.) This coherence amounts to the existence of a faithful functor from categories of this sort freely generated by sets of objects to the category of relations on finite ordinals. Coherence also holds for bicartesian categories where, in addition to this equality for projections, we have that the first and the second injection to the sum of the terminal object with itself are the same. These coherences yield a very easy decision procedure for equality of arrows.
Keywords: Categorial proof theory | Conjunction and disjunction | Decidability of equality of deductions
Publisher: Springer Link

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