Fibrations in category theory are explored through their definitions, properties, and the author's personal journey of understanding the nuances between different interpretations.
About:
Matteo Capucci works in applied category theory, focusing on developing a principled mathematical description of open complex systems, especially those exhibiting agency, such as players in a game, learners and reasoners (cybernetic systems). His tools of choice are formal category theory, dependent types, and graphical syntax.
Website:
Incoming Links:
Outgoing Links:
Subscribe to RSS:
The post argues that the Yoneda lemma cannot effectively address the problem of qualia due to fundamental misunderstandings in category theory.
Categorical cybernetics is a dynamic field that integrates applied category theory with systems theory, focusing on regulation and the potential for innovative research.
Tai-Danae Bradley discusses how enriched category theory can enhance our understanding of language models and their syntactic structures.
The post challenges the myth of opacity in category theory, advocating for the use of generalized elements and morphisms to better understand mathematical structures.
Most mathematicians prioritize practical applications over foundational theories, relying on informal understandings and social constructions rather than rigid formalism.
Category theory serves as a powerful tool for simplifying complex ideas, revealing hidden connections, and fostering standardization across disciplines.
Social structures are the most significant technology humans have developed, enabling progress and human flourishing while often being underestimated in technological discussions.
Effective proof writing in mathematics requires intuition, clarity in understanding theorems, and a willingness to explore and iterate on ideas.
Owen Lynch shares his recent contributions to LocalCharts, focusing on applied category theory and various mathematical concepts.
0New website!
2026-02-24 •
...