University of Birmingham > Talks@bham > Theoretical computer science seminar > Are all substitutions invertible; are all monoids groups?

## Are all substitutions invertible; are all monoids groups?Add to your list(s) Download to your calendar using vCal - Murdoch Gabbay, Heriot-Watt University
- Friday 23 September 2011, 13:00-14:00
- UG40 Computer Science.
If you have a question about this talk, please contact Paul Levy. Clearly, not everything we do in life is reversible. That’s why mathematicians have monoids. However, every monoid can be mapped to a corresponding group in a natural way, so perhaps everything we do in mathematics is reversible after all. This is not obvious. Consider the two-element monoid with elements
{0,1} and 1+1=1. We can naively add an inverse -1 to 1, but then we
quickly derive 1=0; the monoid collapses to the trivial group, which
is not what we intended. I will show how it is nevertheless possible
to get an adjunction between categories of monoids and groups such
that, in a suitable sense, every monoid can be This is joint work with Peter Kropholler in Glasgow. For more information, see www.gabbay.org.uk This talk is part of the Theoretical computer science seminar series. ## This talk is included in these lists:- Computer Science Departmental Series
- Computer Science Distinguished Seminars
- Theoretical computer science seminar
- UG40 Computer Science
- computer sience
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