Abstract

This note explores the intersection of category theory and assemblage theory as frameworks for modeling complex, relational systems in association with methodologies like Cynefin’s SenseMaker and Estuarine mapping which is the base of the Eurosense project. It highlights how category theory’s focus on objects, morphisms, functors and natural transformations provides a universal language for bridging disparate fields, while assemblage theory’s emphasis on dynamic, heterogeneous networks offers a lens for understanding fluid phenomena like social movements or ecological systems. The text further reflects on how standardized Ologs (Ontology Logs) grounded in category theory could address fragmentation in Eurosense by formalizing implicit structures across diverse narratives and mappings, enabling connectivity without imposing uniformity. This could result in a practice of "relational cartography" that embraces the generative potential of partial, situated knowledge, aligning with both theoretical frameworks.

Category theory

Category theory is a mathematical framework that abstracts structures into objects (like sets or groups) and morphisms (arrows representing transformations between them), prioritizing their relationships and composition over internal specifics. By using tools such as functors (which map between categories) and natural transformations (which are morphisms between functors), it offers a universal language to bridge disparate fields—from algebra to logic—by focusing on how systems interact rather than their intrinsic properties. This makes it particularly powerful for modeling interconnected systems, whether in theoretical physics, computer science, or, as in the curent reflection, assemblage theory, where dynamic networks of relations take center stage.

Assemblage theory

Assemblage theory is a philosophical framework that understands complex systems—not as fixed, bounded wholes—but as dynamic assemblages of heterogeneous elements (human, non-human, material, or discursive) that temporarily stabilize through their contingent relations (DeLanda 2019). Drawing from thinkers like Deleuze and Guattari, it emphasizes emergence, multiplicity, and process, rejecting essentialist categories in favor of analyzing how components interact, decompose, or recombine across scales. This makes it especially useful for studying fluid phenomena like social movements, technological networks, or ecological systems, where agency and structure arise from relational configurations rather than pre-given essences.

Cynefin's sensemaker

Assemblage theory serves as a foundational lens for the Cynefin’s SenseMaker and the associated Estuarine mapping by providing a relational ontology that aligns with their core principles of complexity, emergence, and context-dependent sense-making. In the Cynefin framework, assemblages help conceptualize how micro-narratives—collected through SenseMaker—are not isolated data points but dynamic, interconnected fragments of larger socio-cultural systems, where meaning arises from their contingent interactions rather than fixed categories. The theory’s emphasis on multiplicity and temporary stabilization mirrors Cynefin’s domains (Simple, Complicated, Complex, Chaotic), where boundaries are porous, and patterns emerge from decentralized agent interactions—much like how an assemblage’s components (e.g., stories, actors, material constraints) coalesce into fleeting but actionable insights.
Sensemaker is one of the tools developed to address situations in the complex domain and is based on narratives collected through interviews or directly  from a webpage or an application on a smart device. SenseMaker is a form of distributed ethnography, as it transfers the onus of interpretation of narratives from the researcher to participants who are asked to answer a set of questions about their narrative. Through this self-signification, SenseMaker removes ethnographic coding and expert re-interpretation, as participants assign meaning to their own micro-narratives, which enables large scale explorations, reduces researcher bias, and allows for more objective analysis (Van der Merwe et al. 2019) .

Estuarine mapping

Eestuarine mapping draws on assemblage thinking to model systems as fluid, overlapping currents of influence (e.g., institutional policies, grassroots practices, environmental factors), where traditional hierarchical maps fail..Estuarine mapping serves as the initial, exploratory phase in participatory sense-making, designed to identify the actants—human and non-human agents, forces, or entities—operating within a specific context. Unlike traditional mapping techniques that impose predefined categories, Estuarine mapping embraces the situated worldviews of participants, capturing their partial, often contradictory perspectives as they navigate a given problem space (e.g., a community’s response to climate displacement or a policy dispute). This approach acknowledges that any "context" is itself a temporary stabilization of relations rather than a fixed container. By surfacing these actants as they are perceived by participants, the method avoids the pitfalls of external imposition, instead treating the map as a living artifact of collective sense-making, limited to the scope of the session but open to recombination with other contexts.

Eurosense

Eurosense (www.eurosense.eu) aims at enhancing inclusivity in political processes by fostering genuine bottom-up approaches—from identifying challenges to designing solutions. It utilizes the Sensemaker tool based on the Cynefin framework (Snowden and Boone, 2007)—which helps organizations adapt their strategies by categorizing challenges into four domains: simple, complex, complicated, or chaotic.
The goal of  Eurosense is to create a European Sensor Network of localied or distributed communities  that adopt a shared  process involving citizen and stakeholders ( civil society, local administrators, public services and other that may be related to a specific issue) in reflecting on the narratives collected to understand the political and social context they are involved in and identify possible actions aimed at positively influencing it . 
Eurosense operates through the systematic collection, analysis, and interpretation of narratives across a multitude of domains. Its approach transcends traditional boundaries, bridging the gap between qualitative storytelling and quantitative data extraction to uncover deeper insights into human behaviour, societal shifts, and systemic influences. Given the broad range of topics addressed, in order to implement  the systemic self-reflection process  it is necessary to orient  the reflections on specific domains allowing a coherent group of stakeholders to identify actionable ideas. This categorization can be done, among other possible criteria, at the geographical (e.g.: a city, a neighbourhood, ), thematic (e.g. Climate adaptation, Artificial intelligence, ...)  or the level as in the sense of the Multilevel Prespectiveas in (Schlaile et al. 2022).

Using Ologs to connect disparate narratives across contexts

The challenge of navigating a disconnected series of narratives and mappings—emerging from diverse contexts such as participatory workshops, policy analyses, or community storytelling across varied geographical and social settings—is unique to Eurosense compared to traditional sensemaking projects. Addressing this diversity demands a framework that can bridge fragmentation without imposing rigid uniformity. Here, Ologs (Ontology Logs), grounded in Category Theory, may offer a solution by providing a relational scaffolding that honors pluralism while enabling connectivity. Ologs, as categorical diagrams, may allow practitioners to formalize the implicit structures within each context (e.g., a narrative’s actors, a map’s spatial relations, or a policy’s stakeholder dynamics) as objects and morphisms—not to reduce complexity, but to expose shared patterns of interaction across disparities.
Once the actants are identified though the Estuarine based process and workshops, their relationships could be formalized into a Category Theory-based Olog, transforming the estuarine map into a rigorous yet flexible analytical tool. In this framework, actants become objects in a category, while their interactions—whether causal, symbolic, or material—are represented as morphisms (arrows) between them. For example, an Olog might represent a community’s narrative about urban displacement as a network of nodes (e.g., "housing policy," "migrant networks," "gentrification pressures") connected by arrows denoting relationships like "constrains," "enables," or "emerges from." . The actual process is not yet defined, but it could possibly be inspired by the approach of the theory of indeterminate natural transformations (TINT ). applied to metaphors (Fuyama et al. 2020).
By adopting this approach, Eurosense could translate between contexts—linking for example a grassroots map of informal economies in Athens to a policy narrative from Brussels—not through forced alignment, but by identifying isomorphic processes (e.g., how "trust" morphs into "collective action" in both cases). This practice becomes accessible because Ologs can be co-created with non-experts using visual tools (e.g., participatory diagramming), responsive because new contexts can be integrated without overhauling the framework, and pluralist because it accommodates conflicting ontologies (e.g., a municipality’s "official" map and a refugee community’s counter-map) as complementary perspectives within the same categorical lattice.
This formalization enables cross-context comparison: morphisms can be used to assess equivalences between seemingly disjointed situations (e.g., a labor strike in Lisbon and a housing cooperative in Berlin), revealing hidden symmetries or structural homologies. Moreover, by analyzing the commutativity of diagrams (i.e., whether different paths between actants yield consistent outcomes), practitioners can validate the transferability of actions—determining, for instance, if a tactic effective in one context might resonate in another, not because the contexts are sufficiently similar but because their relational logics align. This process doesn’t erase differences; rather, it makes them composable, allowing Eurosense or similar initiatives to navigate pluralism without sacrificing analytical precision.
Crucially, this approach aligns with assemblage theory’s rejection of fixed boundaries: just as an assemblage’s components (e.g., a protest’s slogans, a law’s loopholes, a river’s flooding) gain meaning through their contingent relations, Ologs have the potential to make visible how Eurosense’s disparate narratives and maps are already entangled—not as a pre-existing whole, but as a dynamic, composable system. The ambition is to foster a practice of "relational cartography" where standardization does not homogenize but instead reveals the generative gaps between contexts, transforming disconnection into a resource for collective sense-making.

References

DeLanda, M., 2019. A New Philosophy of Society: Assemblage Theory and Social Complexity. https://doi.org/10.5040/9781350096769
Fuyama, M., Saigo, H., Takahashi, T., 2020. A category theoretic approach to metaphor comprehension: Theory of indeterminate natural transformation. Biosystems 197, 104213. https://doi.org/10.1016/j.biosystems.2020.104213
Schlaile, M.P., Kask, J., Brewer, J., Bogner, K., Urmetzer, S., Witt, A.D., 2022. Proposing a Cultural Evolutionary Perspective for Dedicated Innovation Systems: Bioeconomy Transitions and Beyond PERSO. Journal of Innovation Economics & Management 38, 93–118. https://doi.org/10.3917/e.jie.pr1.0108
Snowden, D.J., Boone, M.E., 2007. A Leader’s Framework for Decision Making. Harvard Business Review.
Van der Merwe, S.E., Biggs, R., Preiser, R., Cunningham, C., Snowden, D.J., O’Brien, K., Jenal, M., Vosloo, M., Blignaut, S., Goh, Z., 2019. Making Sense of Complexity -  Using SenseMaker as a Research Tool. Systems 7, 25. https://doi.org/10.3390/systems7020025