The Exchange Property in Grothendieck Categories: Applications |
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| Authors: | L Dăuş C Năstăsescu M Salim |
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| Affiliation: | 1. Department of Mathematical Sciences, United Arab Emirates University, Al Ain, UAEleonard.daus@uaeu.ac.ae;3. “Simion Stoilow” Institute of Mathematics, Romanian Academy, Bucharest, Romania;4. Department of Mathematical Sciences, United Arab Emirates University, Al Ain, UAE |
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| Abstract: | We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property. |
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| Keywords: | Coalgebra Exchange property Grothendieck category Graded module Suitable ring |
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