


Towards a calculus of fractions concerning Kaninjectivity



Description: 
In an orderenriched 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 Kaninjective. 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 KockZoberlein 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: 
20140624

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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