ON DESCENT FOR COALGEBRAS AND TYPE TRANSFORMATIONS

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KIANPI MAURICE

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Journal Paper

Paper Information

Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2016 | Volume:5 | Issue:1 Page(s): 103-129

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Information Journal Paper

Title

ON DESCENT FOR COALGEBRAS AND TYPE TRANSFORMATIONS

Author(s)

KIANPI MAURICE | Issue Writer Certificate

Keywords

CATEGORYQ4

FUNCTORQ4

COALGEBRAQ4

NATURAL TRANSFORMATIONQ4

(CO)LIMITSQ4

(EFFECTIVE) DESCENT MORPHISMQ4

Abstract

We find a criterion for a morphism of COALGEBRAs over a Barr- exact CATEGORY to be effective descent and determine (effective) descent mor- phisms for COALGEBRAs over toposes in some cases. Also, we study some ex- actness properties of endofunctors of arbitrary categories in connection with NATURAL TRANSFORMATIONs between them as well as those of FUNCTORs that these transformations induce between corresponding categories of COALGEBRAs. As a result, we find conditions under which the induced FUNCTORs preserve natural number objects as well as a criterion for them to be exact. Also this enable us to give a criterion for split epis in a CATEGORY of COALGEBRAs to be effective descent.

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