Terminal Coalgebras for Measure-Polynomial Functors

2009 ◽  
pp. 325-334 ◽  
Author(s):  
Christoph Schubert
Keyword(s):  
Polynomial Functors

scholarly journals The monoidal structure on strict polynomial functors

2017 ◽  
Vol 485 ◽  
pp. 213-229 ◽  
Author(s):  
Cosima Aquilino ◽  
Rebecca Reischuk
Keyword(s):  
Monoidal Structure ◽  
Polynomial Functors

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

Ext-groups in the Category of Strict Polynomial Functors

2019 ◽  
Author(s):  
Van Tuan Pham
Keyword(s):  
Orthogonal Groups ◽  
Explicit Formulas ◽  
Polynomial Functors ◽  
Ext Groups

Abstract The aim of this paper is to study, by using the mathematical tools developed by Chałupnik, Touzé, and Van der Kallen, the effect of the Frobenius twist on $\operatorname{Ext}$-group in the category of strict polynomial functors. As an application, we obtain explicit formulas of cohomology of the orthogonal groups and symplectic ones.

scholarly journals Polynomial Functors from Algebras Over a Set-Operad and Nonlinear Mackey Functors

2013 ◽  
Vol 2015 (6) ◽  
pp. 1461-1554 ◽  
Author(s):  
Manfred Hartl ◽  
Teimuraz Pirashvili ◽  
Christine Vespa
Keyword(s):  
Polynomial Functors ◽  
Mackey Functors

A note on polynomial functors and ext1Groups

1997 ◽  
Vol 25 (3) ◽  
pp. 979-987
Author(s):  
Geoffrey M. L. Powell
Keyword(s):  
Polynomial Functors

scholarly journals Polynomial functors and polynomial monads

2012 ◽  
Vol 154 (1) ◽  
pp. 153-192 ◽  
Author(s):  
NICOLA GAMBINO ◽  
JOACHIM KOCK
Keyword(s):  
Basic Theory ◽  
Polynomial Functors ◽  
Cartesian Closed Categories ◽  
Cartesian Closed ◽  
The Relationship

AbstractWe study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

scholarly journals A duality for polynomial functors

1995 ◽  
Vol 104 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Vincent Franjou ◽  
Jeffrey H. Smith
Keyword(s):  
Polynomial Functors

scholarly journals Free resolutions for polynomial functors

2004 ◽  
Vol 271 (1) ◽  
pp. 22-64 ◽  
Author(s):  
Alexandre Tchernev ◽  
Jerzy Weyman
Keyword(s):  
Free Resolutions ◽  
Polynomial Functors
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