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5 unusual facts about André Joyal


André Joyal

A. Joyal, Ross Street, An introduction to Tannaka duality and quantum groups, Category theory (Como, 1990), 413—492, Lecture Notes in Math.

Combinatorial proof

An alternative bijective proof, given by Aigner and Ziegler and credited by them to André Joyal, involves a bijection between, on the one hand, n-node trees with two designated nodes (that may be the same as each other), and on the other hand, n-node directed pseudoforests.

Jacob Lurie

Infinity categories (in the form of Joyal's quasi-categories) are a convenient framework to do homotopy theory in abstract settings.

Kripke semantics

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.

Pseudoforest

André Joyal used this fact to provide a bijective proof of Cayley's formula, that the number of undirected trees on n nodes is nn − 2, by finding a bijection between maximal directed pseudoforests and undirected trees with two distinguished nodes.



see also