* A Note on the Smash Product and Regular Associativity
@ 2024-10-23 8:14 Marco Grandis
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From: Marco Grandis @ 2024-10-23 8:14 UTC (permalink / raw)
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This article is published online, in APCS:
A Note on the Smash Product and Regular Associativity
Marco Grandis
Applied Categorical Structures (2024) 32:33. October 2024
DOI: 10.1007/s10485-024-09787-8
Link (only view): https://rdcu.be/dXwfe<https://url.au.m.mimecastprotect.com/s/cf4hC1WLjwsMEDgyxfGhmFVA51b?domain=rdcu.be>
Abstract. We want to study the smash product of pointed topological spaces, in an organic way and full generality, without relying on some ‘convenient subcategory’. The n-ary smash product has a ‘colax’ form of associativity, which supplies a categorical framework for the properties of this operation and its connection with the function spaces. Various concrete computations of smash products are given, including a large class of cases where associativity fails. Lax and colax monoidal structures are unusual and interesting, in category theory. Some parts of this note will be obvious to a topologist and others to a categorist, in order to take into account both backgrounds.
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Regards,
Marco Grandis
New email address:
grandismrc@gmail.com
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