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Martin Sleziak
Martin Sleziak
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Pretty much anyone who does algebra is familiar with group objects in categories, but what about cogroup objects? Most of what I've been able to find about them is that they "arise naturally in algebraic topology" (from wikipediawikipedia) and that, somehow, the n-sphere is one (nLabnLab's meager entry). Is there a reference for more on the stuff? Specifically wondering if the spaces of pointed maps from a topological space X to a pointed sphere are cogroups, and if anything is known about these "cohomotopy groups."

Pretty much anyone who does algebra is familiar with group objects in categories, but what about cogroup objects? Most of what I've been able to find about them is that they "arise naturally in algebraic topology" (from wikipedia) and that, somehow, the n-sphere is one (nLab's meager entry). Is there a reference for more on the stuff? Specifically wondering if the spaces of pointed maps from a topological space X to a pointed sphere are cogroups, and if anything is known about these "cohomotopy groups."

Pretty much anyone who does algebra is familiar with group objects in categories, but what about cogroup objects? Most of what I've been able to find about them is that they "arise naturally in algebraic topology" (from wikipedia) and that, somehow, the n-sphere is one (nLab's meager entry). Is there a reference for more on the stuff? Specifically wondering if the spaces of pointed maps from a topological space X to a pointed sphere are cogroups, and if anything is known about these "cohomotopy groups."

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YCor
YCor
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Cogroup Objectsobjects

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Charles Siegel
Charles Siegel
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Cogroup Objects

Pretty much anyone who does algebra is familiar with group objects in categories, but what about cogroup objects? Most of what I've been able to find about them is that they "arise naturally in algebraic topology" (from wikipedia) and that, somehow, the n-sphere is one (nLab's meager entry). Is there a reference for more on the stuff? Specifically wondering if the spaces of pointed maps from a topological space X to a pointed sphere are cogroups, and if anything is known about these "cohomotopy groups."