# Public:Comonad Resources

## Publications

Papers

- Samson Abramsky, Anuj Dawar, and Pengming Wang. "The pebbling comonad in finite model theory." 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2017. arXiv:1704.05124
- Anuj Dawar, Simone Severini, and Octavio Zapata. "Pebble games and cospectral graphs." Electronic Notes in Discrete Mathematics 61 (2017): 323-329. doi
- Samson Abramsky and Nihil Shah. "Relating Structure and Power: Comonadic semantics for computational resources." International Workshop on Coalgebraic Methods in Computer Science. Springer, Cham, 2018. arXiv:1806.09031
- Samson Abramsky. "Whither semantics?." Theoretical Computer Science 807 (2020): 3-14.
- Samson Abramsky, Dan Marsden. "Comonadic semantics for guarded fragments." arXiv:2008.11094
- Thomas Paine. "A Pebbling Comonad for Finite Rank and Variable Logic, and an Application to the Equirank-variable Homomorphism Preservation Theorem." Electronic Notes in Theoretical Computer Science, 352, 191-209. doi
- Adam Ó Conghaile, Anuj Dawar. "Game Comonads & Generalised Quantifiers." arXiv:2006.16039
- Samson Abramsky and Nihil Shah. "Relating Structure and Power: Extended Version" arXiv:2010.06496
- Anuj Dawar. "Constraint Satisfaction, Graph Isomorphism, and the Pebbling Comonad." to appear
- Samson Abramsky, Luca Reggio. "Arboreal Categories: An Axiomatic Theory of Resources." arXiv:2102.08109
- Anuj Dawar, Tomáš Jakl, Luca Reggio. "Lovász-type Theorems and Game Comonads." arXiv:2105.03274
- Nihil Shah, "Restricting Power: The Pebble-Relation Comonad in Finite Model Theory." ACT 2021 paper

Theses/reports:

- Nihil Shah: Game Comonads in Finite Model Theory (Master Thesis) [1]
- Adam Ó Conghaile: Game comonads, descriptive complexity & finite model theory (First Year Report) [2]

## Talks (slides and/or videos)

- Nihil Shah, "Restricting Power: The Pebble-Relation Comonad in Finite Model Theory" at ACT 2021 (slides, video).
- Luca Reggio (j.w.w. Anuj Dawar, Tomáš Jakl) "Lovász-type Theorems and Game Comonads" at LICS 2021 [3].
- Daniel Marsden (j.w.w. Samson Abramsky) "Comonadic semantics for guarded fragments" at LICS 2021 [4].
- Nihil Shah. "Bisimulation between hom sets and logics without counting" at Structure meets Power workshop 2021 (slides, video).
- Luca Reggio. "Lovász-type theorems and polyadic spaces" at BLAST 2021 (slides).
- Thomas Paine. "Game Comonads and an application to the Equirank-variable conjecture" at MFPS 2020 [5].
- Adam Ó Conghaile. "k-Cores for game comonads" at Contextuality 2019 (slides).

- Dan Marsden: Guards, Structure and Power
- Adam Ó Conghaile: Game comonads and generalised quantifiers
- Nihil Shah: Path-width and restricting conjunction in k-variable logic

Samson's talks on the topic:

- Coalgebra Dreams [6]
- Relating Structure to Power:Comonadic semantics for computational resources [7]

Related:

- Nihil Shah - Cofree Comonads and their Uses (at LamdaConf), recording on youtube