Conservativity of duals

Abstract: Dual objects in monoidal categories have many applications, including channels in parallel programming, input-output modes in logic programming, and string diagrams for internal-homs. Thus, it is natural to ask whether duals intrinsically strengthen the theory, i.e. whether monoidal categories with duals are "conservative", in a suitable sense, over monoidal categories without duals. While "compact closed" duals are not generally conservative, we show that "∗-autonomous" duals frequently are: in particular, the free extension of any closed symmetric monoidal category to a ∗-autonomous category is a fully faithful embedding. Thus, "richer" languages with ∗-autonomous duals can be unambiguously used to reason about "poorer" languages that lack them.

This talk is about the same paper as my talk at ACT@UCR, but the talks will be complementary, with no expectation that anyone attending this talk has seen the other one.

category theory

Audience: advanced learners

( paper | slides )

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MIT (applied) categories seminar

Series comments: The MIT Categories Seminar is an informal teaching seminar in category theory and its applications, with the occasional research talk. We presently meet online each Thursday, 12noon to 1pm Boston time (UTC-4). The talk is broadcast over Zoom and YouTube, with simultaneous discussion on the Category Theory Zulip channel. (To join the channel, click here.) Talks are recorded and remain available on our YouTube channel. Our Google Calendar is here.

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