Presenting Finite Posets

We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of generators and relations, we construct a presentation of our category, which corresponds to a variant of the notion of bialgebra.

[1]  Romain Beauxis,et al.  A Non-Standard Semantics for Kahn Networks in Continuous Time , 2011, CSL.

[2]  Felix Hueber,et al.  Locally Presentable And Accessible Categories , 2016 .

[3]  Samuel Mimram,et al.  Towards 3-Dimensional Rewriting Theory , 2014, Log. Methods Comput. Sci..

[4]  Samuel Mimram,et al.  The Structure of First-Order Causality , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[5]  A. Joyal,et al.  The geometry of tensor calculus, I , 1991 .

[6]  Samuel Mimram,et al.  Asynchronous Games: Innocence Without Alternation , 2007, CONCUR.

[7]  Ieke Moerdijk,et al.  Dendroidal Sets , 2007, math/0701293.

[8]  Viggo Stoltenberg-hansen,et al.  In: Handbook of Logic in Computer Science , 1995 .

[9]  Yves Lafont,et al.  Towards an algebraic theory of Boolean circuits , 2003 .

[10]  Albert Burroni,et al.  Higher-Dimensional Word Problems with Applications to Equational Logic , 1993, Theor. Comput. Sci..

[11]  Ieke Moerdijk,et al.  Tensor product of dendroidal sets , 2010 .

[12]  John Power,et al.  Symmetric monoidal sketches , 2000, PPDP '00.

[13]  J. Benabou.  Introduction to bicategories , 1967 .

[14]  Ross Street,et al.  Limits indexed by category-valued 2-functors , 1976 .

[15]  Mogens Nielsen,et al.  Models for Concurrency , 1992 .

[16]  S. Maclane,et al.  Categorical Algebra , 2007 .

[17]  Teimuraz Pirashvili.  On the PROP corresponding to bialgebras , 2001 .

[18]  Marcelo P. Fiore,et al.  The Algebra of Directed Acyclic Graphs , 2013, Computation, Logic, Games, and Quantum Foundations.

[19]  E. Szpilrajn.  Sur l'extension de l'ordre partiel , 1930 .

[20]  Prakash Panangaden,et al.  Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky , 2013, Lecture Notes in Computer Science.

[21]  A. Power,et al.  A 2-categorical pasting theorem , 1990 .

[22]  Samuel Mimram.  Sémantique des jeux asynchrones et réécriture 2-dimensionnelle. (Asynchronous Game Semantics and 2-dimensional Rewriting Systems) , 2008 .