Generic morphisms, parametric representationsand weakly cartesian monads
By Mark Weber. Theory and Applications of Categories, 2004
74 citations recorded by the source corpus.
Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined. Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c69f586a080ac96c47a8fd90f398e5b5f927d2de
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In Algebra and Number Theory
- Imma G'alvez-Carrillo
- Joachim Kock
- Nicola Gambino
- Andrew Tonks
- Ben Webster
- Bob Coecke
- Andrew Justin Blumberg
- M. Hill
In Geometry and Topology
- Nicola Gambino
- Imma G'alvez-Carrillo
- Andrew Tonks
- Joachim Kock
- Ben Webster
- Bob Coecke
- Andrew Justin Blumberg
- M. Hill
In Mathematical Physics
- Nicola Gambino
- Imma G'alvez-Carrillo
- Andrew Tonks
- Joachim Kock
- Ben Webster
- Bob Coecke
- Andrew Justin Blumberg
- M. Hill
Citations in the corpus
- Polynomial Functors and Trees (2008, background): “With Proposition 2.2.10 we are in position to apply Weber’s general nerve theorem (2.0.5) directly, establishing this: 2.2.12 Theorem.”
- Polynomial functors and polynomial monads (2009, background): “The associated polynomial functor PM(Xi | i ∈ I ) = ⎛⎝ ∑ m∈M j Xs(m) | j ∈ J ⎞⎠”
- Familial 2-functors and parametric right adjoints (2007, unknown): “Recall from [38] that f : B→T A is T -generic when for any α, β, and γ making the outside of B α G G f T X T γ T A T β G G T δ ` ` T Z commute, there is a unique 6 δ for which γ • δ = β and T (δ) • f = α.”
- Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory (2015, background): “A recommended entry point to the theory is Berger–Melliès–Weber [6].”
- Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness (2015, background): “The notions of generic and free maps are general notions in category theory, introduced by Weber [34, 35], who extracted the notions from earlier work of Joyal [17]; a recommended entry point to the theory is Berger–Melliès–Weber [3].”