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Biunit pairs are introduced as pairs of elements in a semiheap thatgeneralize the notion of unit. Families of functions generalizing involutionsand conjugations, called switches and warps, are investigated. The main theoremestablishes that there is a one-to-one correspondence between monoids equippedwith a particular switch and semiheaps with a biunit pair. This generalizes awell-established result in semiheap theory that connects involuted semigroupsand semiheaps with biunit elements. Furthermore, diheaps are introduced assemiheaps whose elements belong to biunit pairs and they are shown to benon-isomorphic but warp-equivalent to heaps.

Biunit pairs in semiheaps and associated semigroups