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Mercredi 30 Août
| Heure: |
11:00 - 12:30 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Coherence for skew near-semiring categories |
| Description: |
Tarmo Uustalu We consider skew near-semiring categories, a relaxation of
near-semiring categories where the unitors, associators, annihilator
and distributor are not required to be natural isomorphisms, they
are just natural transformations in a particular direction. We
prove a coherence theorem for such categories. The theorem states
that, in a free skew near-semiring category over a set of objects,
any two maps between an object and an object in normal form are
equal.
Our main motivating examples for skew near-semiring categories are from programming with effects. While (relative) monads and lax monoidal functors are the same as skew monoids in particular skew monoidal categories, (relative) MonadPlus and Alternative instances are skew near-semiring objects.
This is joint work with Mauro Jaskelioff, Exequiel Rivas and Niccolò Veltri. |
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