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Towards a calculus of fractions concerning Kan-injectivity

Description:  In an order-enriched category $\cal X$, for a given subcategory $\cal A$, we study the class ${\cal A}^{KInj}$ of all morphisms with respect to which $\cal A$ is Kan-injective. We show that, for $\cal A$ an arbitrary subcategory of $\cal X$, ${\cal A}^{KInj}$ is, in a certain sense, closed under weighted colimits. In the case of $\cal A$ being a Kock-Zoberlein monadic subcategory of $\cal X$, we construct a category of "fractions" for the class of morphisms ${\cal A}^{KInj}$. Here, "fractions" for a morphism $h$ refers to the existence of a morphism $h_*$ such that $h_* h=id$ and $h h_*\le id$. This construction resembles the one of a category of fractions for the class of morphisms inverted by a reflector into a full reflective subcategory.
Date:  2014-06-24
Start Time:   14:30
Speaker:  Lurdes Sousa (CMUC and IP Viseu)
Institution:  CMUC, IP Viseu
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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